Mathematics

Research area: My specialized research area is community-oriented artificial intelligence, mathematical modeling, and data science for infectious disease prevention, preparedness, and response. I develop AI-enabled and mathematical modeling approaches to support public-health decision-making, with emphasis on epidemic dynamics, behavioral responses, vaccination strategies, climate and environmental drivers, and health equity. This research integrates epidemiological data, climate-informed modelling, and community-relevant analytics to address infectious disease challenges in Canada, Africa, and the Global South, while supporting resilient health systems and equitable outbreak response.

Student roles:
The student will review literature on category theory, multimodal learning, AI security, and data poisoning, then help develop a formal framework for representing multimodal pipelines as objects, morphisms, and compositional structures. They will design algorithmic prototypes to detect inconsistencies, trace poisoned data propagation, and evaluate mitigation strategies using simulated or real-world multimodal tasks. The student will analyze results, prepare visualizations, document methods, and contribute to manuscript writing in collaboration with supervisors and interdisciplinary partners.

Skills required:
The ideal student should have a background in mathematics, applied mathematics, computer science, artificial intelligence, machine learning, data science, cybersecurity, statistics, or a related field. Familiarity with category theory, abstract algebra, linear algebra, probability, multimodal learning, AI security, and data poisoning is preferred. Experience with Python, R, Julia, MATLAB, or machine-learning libraries would be an asset. Strong mathematical reasoning, coding, analytical, writing, and communication skills are required.

Research area: Our research lies in mathematical epidemiology, focusing on multiscale modeling of infectious and chronic diseases. We develop dynamical systems that integrate within-host immune dynamics, population-level transmission, and social determinants of health, with applications to vector- borne diseases, syndemics, and comorbidity dynamics. Our work incorporates climate-driven processes, host-pathogen interactions, and health inequities. Methodologically, we use applied differential equations, singular perturbation theory, and data-driven approaches such as Bayesian inference. We also integrate artificial intelligence and machine learning, including neural differential equations, to enhance model calibration, flexibility, and predictive capability.

Student roles:
The student will play an active role in developing, implementing, and analyzing a syndemic
model of diabetes and comorbidities. The project will begin with data collection and
preprocessing, where the student will compile epidemiological and socioeconomic data from
Statistics Canada and Public Health Ontario. This includes preparing datasets on diabetes
prevalence, comorbidity rates, and key social determinants such as income and healthcare access.
The student will implement the mathematical model computationally using R, Python, or
MATLAB, incorporating disease progression pathways and interactions between conditions. A
major component of the role involves parameter estimation using Bayesian inference techniques,
including implementation of Markov Chain Monte Carlo (MCMC) methods to calibrate the
model to observed data.
The student will conduct sensitivity and uncertainty analyses to identify the most influential
parameters and assess the robustness of model predictions. They will also perform scenario
analyses to evaluate the impact of interventions, such as improved healthcare access or reduced
socioeconomic disparities, on disease burden.
In addition, the student will contribute to model validation by comparing simulation outputs with
empirical data and refining the model as needed. Documentation of methods, code development,
and interpretation of results will be expected throughout the project.
The student will participate in regular research discussions and contribute to the preparation of a
final report, a manuscript for publication, and conference presentations. This role provides
valuable interdisciplinary experience at the interface of mathematics, data science, and public
health, with a strong emphasis on health equity.

Skills required:
The student should have a strong background in mathematics, statistics, epidemiology, or a
related quantitative field. Familiarity with differential equations, dynamical systems, and basic
disease modeling is required. Experience with programming in R, Python, or MATLAB is
essential. Knowledge of statistical inference methods, particularly Bayesian approaches, is
desirable. An interest in public health, health equity, or social determinants of health will be an
asset. Strong analytical, problem-solving, and scientific communication skills are expected.

Research area: Emerging Space and Network Systems: Space-Air-Ground Integrated Systems, Satellites & Constellations, Non-Terrestrial Networks (NTN), Protocols/Architecture/Management, Resilience & Sustainability, 6G NTN, IoT, Quantum Networks Applied AI/Machine Learning: Autonomous Networking, Embedded AI, Edge AI/Computing, Anomaly Detection Systems & Applications for Real-World Challenges: Digital Divide, Digital Health, Smart Agriculture/Aquaculture, Environmental Monitoring, Industry 5.0, etc.

Student roles:
• Design and develop software prototypes using Python, incorporating custom modules and state-of-the-art AI/ML frameworks.
• Investigate key research challenges in NTNs using advanced AI/ML techniques, including data-driven modeling and optimization.
• Diagnose and resolve technical issues independently, demonstrating strong problem-solving skills and initiative.
• Critically review and synthesize academic literature to inform research directions and methodologies.
• Contribute to the preparation of technical reports, research papers, and publications in leading venues.

Skills required:
• Strong proficiency in Python programming, with hands-on experience using modern machine learning frameworks (e.g., PyTorch) and related libraries.
• Solid background in one or, preferably, a combination of the following areas: (1) deep learning (DL) or reinforcement learning (RL), (2) wireless communications and networking, (3) AI hardware (e.g., FPGA, GPU/TPU), (4) quantum computing, sensing, or networking, and (5) aerodynamic analysis.
• Demonstrated ability to work independently with a high level of self-motivation, as well as collaborate effectively within a multidisciplinary team.
• Strong academic research skills, including critical thinking, literature review, and scholarly writing.

Research area: 3D Gaussian Splatting (3DGS) reconstructs 3D scenes from images and enables real-time novel-view rendering. However, its training with first-order methods like SGD and Adam can be slow as millions of Gaussian parameters with different units (position, scale, rotation, opacity, and colour) interact nonlinearly, creating an ill-conditioned loss landscape. This project explores approximate natural-gradient descent (NGD) methods for accelerating 3DGS. The key idea in NGD is to adapt updates to the function-space geometry using curvature information of the loss landscape, scaled with Kronecker-factored curvature approximations. The intern will prototype and benchmark these methods against Adam.

Student roles:
You will work as a junior research developer in a single, clearly defined role: prototype and evaluate optimizers for 3D Gaussian splatting. Day-to-day work will include reading background material, implementing optimizer components, debugging experiments, collecting results, discussing findings with your supervisor, and compiling them into a scientific report.

Skills required:
Required:
- Familiarity with PyTorch, neural network training and logging on GPUs, as well as basic training algorithms like SGD and Adam

Helpful but not required:
- Familiarity with optimization, specifically second-order methods (Newton's method, natural gradient descent, K-FAC)
- Familiarity with applications of Gaussian splatting in computer vision

Research area: My research is in physics-based animation, the branch of computer graphics concerned with simulating the motion of physical systems like deformable solids, cloth, fluids, and the contact between them. The work sits at the intersection of continuum mechanics, numerical optimization, and high-performance computing: we discretize the governing equations of motion, design solvers that are stable and fast under large time steps, and balance physical accuracy against the interactive performance that graphics applications demand. PhySherGraph, an in-house simulation framework, serves as the common platform for these projects, which lets interns build onto rather than start from scratch.

Student roles:
The intern will develop the adaptive thin-shell simulator from research to working implementation. The first weeks are devoted to studying the relevant literature, including discrete shell models for bending and stretching, adaptive remeshing strategies for cloth, and the mesh-shader programming model, and to familiarizing themselves with PhySherGraph's existing simulation and rendering infrastructure. With that grounding, they will design the system's components: the shell energy and its forces, the refinement indicators, and the mesh-shader subdivision stage with consistent transfer of simulation state.

Implementation proceeds incrementally and is validated at each step. The student will first reproduce a stable uniform thin-shell simulation, then add static refinement driven by the indicators, then dynamic refinement and coarsening that follow wrinkles as they move, checking energy behaviour and visual quality against established baselines as they go. Once the adaptive simulator runs, they will profile it and compare cost and accuracy against a uniformly fine reference. Throughout, they are responsible for clean, documented, reusable code that follows the lab's conventions.

The intern will work on a shared codebase at the heart of my team. They will have regular meetings with me and with the lab members, and develop the communication skills that graduate research demands. By the end of the 12 weeks, the student will deliver a documented adaptive thin-shell module, a quantitative evaluation of its quality and performance, and a short written report suitable as the seed of a research paper, a genuine and self-contained research contribution that previews graduate study in my group.

Skills required:
Strong C++ and hands-on GPU programming experience are essential, ideally with modern graphics APIs (Vulkan, DirectX 12, or WebGPU) and compute or mesh shaders. The candidate should have a solid foundation in linear algebra, numerical methods, and 3D mathematics, and be comfortable reading and extending a substantial existing codebase. No prior cloth-simulation experience is required, but it would be an interesting asset.

Research area: I have over 15 years of experience in statistical methods, Bayesian computation, machine learning, artificial intelligence, statistical quantum, and complex survey designs. My research spans biostatistics, intelligent medicine, manufacturing, statistical physics, and fisheries science. I have contributed to more than 35 peer-reviewed publications and have extensive experience mentoring students and leading interdisciplinary research in mathematics, statistics, and data science.

Student roles:
The student will play a key role in developing and applying advanced statistical and machine learning techniques to genomic and environmental data. Responsibilities include managing and preprocessing data, applying generalized linear and additive models, Bayesian hierarchical models, mixed-effects methods, and machine-learning algorithms. The student will also conduct simulation studies and analyze large-scale genomic datasets. In addition, they will interpret results, prepare reports and manuscripts, present findings at scientific meetings, and collaborate with the research team. These activities will provide the student with interdisciplinary training in statistical genomics, artificial intelligence, and environmental data science.

Skills required:
The student should have a background in statistics, mathematics, computer science, physics, electrical engineering, biology, or a related quantitative discipline. Basic understanding of statistical analysis, programming (in R or Python), and data science is preferred. While experience with genomics or environmental data is helpful, it is not mandatory. The project offers training in statistical genomics, Bayesian modeling, generalized mixed-effects models, machine learning, quantum deep learning, and high-performance computing. Motivated students with strong analytical and problem-solving abilities are encouraged to apply.

Research area: I have over 15 years of experience in statistical methods, Bayesian computation, machine learning, artificial intelligence, statistical quantum, and complex survey designs. My research spans biostatistics, intelligent medicine, manufacturing, statistical physics, and fisheries science. I have contributed to more than 35 peer-reviewed publications and have extensive experience mentoring students and leading interdisciplinary research in mathematics, statistics, and data science.

Student roles:
The student will help develop and apply computational and statistical techniques for analyzing genomic data related to Alzheimer's disease. Responsibilities include programming in Python and R, data processing, exploratory analysis, implementing Bayesian variable selection models, and assessing model performance. The student will also assist in creating and testing hybrid quantum-classical machine learning methods, such as Quantum Generative Adversarial Networks, to model disease progression and intricate genomic patterns. Also, the student will attend research meetings, interpret results, generate visualizations, and aid in preparing scientific reports and presentations.

Skills required:
Applicants are welcome from backgrounds in mathematics, statistics, Physics, and programming experience in Python, R, or similar scientific computing languages. Strong analytical and critical-thinking skills are essential. An interest in machine learning, artificial intelligence, data science, or computational modeling is desirable. Students should be motivated to learn ML and AI methods and apply mathematics and programming to solve challenging real-world problems in biomedical and genomic research.

Research area: My specialized research area is community-oriented artificial intelligence, mathematical modeling, and data science for infectious disease prevention, preparedness, and response. I develop AI-enabled and mathematical modeling approaches to support public-health decision-making, with emphasis on epidemic dynamics, behavioral responses, vaccination strategies, climate and environmental drivers, and health equity. This research integrates epidemiological data, climate-informed modelling, and community-relevant analytics to address infectious disease challenges in Canada, Africa, and the Global South, while supporting resilient health systems and equitable outbreak response.

Student roles:
The student will develop and analyze advanced-time epidemic models in which disease dynamics or intervention decisions depend on expected future outcomes. They will formulate systems of equations, conduct mathematical and computational analyses, run simulations, and compare reactive and anticipatory public-health strategies. The student will explore applications such as ICU capacity planning, vaccination scheduling, and early intervention design. They will prepare figures, interpret results, contribute to presentations and manuscript writing, and meet regularly with supervisors and interdisciplinary collaborators.

Skills required:
The ideal student should have a background in mathematics, applied mathematics, mathematical epidemiology, public health, statistics, data science, computational biology, systems science, operations research, or a related field. Familiarity with differential equations, infectious disease modelling, numerical simulation, forecasting, stability analysis, and public-health decision-making is preferred. Experience with Python, R, MATLAB, Julia, or similar computational tools would be an asset. Strong mathematical reasoning, analytical, coding, writing, and communication skills are required.

Research area: My area is continuous optimization. In particular, I focus on optimization algorithms, including their design, convergence/complexity analysis and efficient implementation, for solving problems arising in machine learning and data science. My research uses theoretical tools from convex analysis, monotone operator theory, applied probability and theoretical computer science. Moreover, my interests also concern efficient implementation of optimization algorithms in modern large scale computing platforms.

Student roles:
The student will be responsible for reading research papers, which will be mathematical and computational, that contain the algorithms that we will study and then implement them in the appropriate computational platform (such as Julia or Python). This will involve many meetings between the PI and the student for trouble-shooting and debugging as well as studying algorithms and analyses from papers. During this process, there will be regular meetings between the PI and the student. The student will be a part of the research group of PI which involves multiple graduate students, with potential collaboration opportunities. The student will show their progress to the PI and to the group via presentations and written reports.

Skills required:
The student is required to have mathematical maturity to be able to read and understand highly mathematical papers that develop optimization algorithms and their convergence analysis. Particularly, the PI expects proficiency with optimization theory, machine learning, linear algebra, probability and real analysis. The main goal of the project is computational: as a result, the student is expected to be proficient with programming languages and environments including Julia, Python, C/C++, PyTorch.

Research area: I am broadly interested in the arithmetic of elliptic curves. Many questions I study lie at the intersection of Iwasawa theory and arithmetic statistics. Iwasawa theory is a branch of algebraic number theory that studies the growth of arithmetic objects, such as ideal class groups or Selmer groups of elliptic curves, in infinite towers of number fields. A long-term goal is to understand the average behaviour of the Iwasawa invariants in appropriate families. I am also interested in questions pertaining to Iwasawa theory of graphs. I also think about questions related to Diophantine stability and Hilbert’s 10th Problem.

Student roles:
The student will spend some time learning the background material before pursuing independent and original research in this area; this will include reading textbooks and research-level published articles. Aside from discussing with me, they will have an opportunity to also interact and discuss mathematics with my graduate students.

The student will perform many computer experiments to obtain data. Based on this, they will formulate precise conjectures. They will try to prove some of the conjectures they formulate. Along the way, I will provide regular guidance.

They will write a written report of their findings, and if they make enough progress I will provide guidance and support to try and publish the results.

Skills required:
1. It would benefit the student if they have some background in algebraic (and analytic) number theory. Knowledge of the theory of elliptic curves is not required, but useful.
2. If the student is somewhat comfortable using Python, C, C++, or SAGE/ PARI/GAP/MAGMA that would be advantageous
3. Most important is to come with an open mind.

Research area: Computer algebra is a relatively recent area in computer science and mathematics, though its roots go back at least forty years. Whereas numerical computations are well-established to be efficient in many cases, computer algebra strives to address the different and arguably more difficult problem of providing exact solutions, or solutions parameterized by variables in the input. There has been an enormous amount of applications in computer science, mathematics, as well as in engineering and education. My research focus on efficient algorithms in matrix, tensor and polynomial computations, Groebner bases, automated theorem prover, and their applications.

Student roles:
In the first three weeks, students will learn the basic programming skill of Prover9 and study some related research papers. After that, students will help me to implement and design algorithms, analysis the output data, and write up the results as human proofs. Students will work with my current research term members including graduate students and undergraduate summer research students. Learning the design and implementation of algorithms will provide high quality training for the students.

Skills required:
Students have already taken some advanced algebra courses. Computer programming skill is preferred but not required.

Research area: Our lab works at the intersection of mathematical epidemiology, scientific machine learning, and numerical analysis. We develop physics-informed neural networks for solving differential equations arising in disease modelling and other scientific applications. A central focus is on training methods that improve the reliability and convergence of these networks when the data and physics objectives conflict. We have recently proposed an adaptive gradient method that detects and manages such conflict during training, and we are currently extending this work to establish its broader applicability across classical partial differential equation systems drawn from physics and engineering.

Student roles:
The intern will join the DIMMS Lab as a research contributor and will work on a focused, self-contained extension of our ongoing research programme. The role is primarily computational, with clearly defined weekly milestones scoped for a twelve-week internship. During the first two weeks, the intern will onboard by reading our published paper on the adaptive gradient method, reviewing the existing codebase, and learning the basics of PINN training through short tutorial notebooks we will provide. By the end of week two, the intern should be able to reproduce our original epidemiological experiment independently. From weeks three to nine, the intern will implement the method on the selected PDE benchmarks, one at a time. For each benchmark, the intern will set up the neural network architecture, define the loss functions, integrate our adaptive gradient method, run training experiments across multiple random seeds, and produce comparison plots against baseline methods. The intern will meet weekly with the supervising faculty and the PhD student to review progress and discuss challenges. During weeks ten to twelve, the intern will consolidate all benchmark results into a single coherent analysis, produce publication-quality figures and tables, and write a draft results section summarizing the findings. The intern will present their work to the DIMMS Lab in a final seminar. Throughout the internship, the intern will be expected to work independently on coding tasks, document their experiments in version-controlled notebooks, and communicate results clearly. We will provide all computing resources, the supervising team's guidance, and access to the lab's GPU workstation. The intern will be treated as a full member of the research team and is encouraged to contribute ideas and suggest methodological improvements.

Skills required:
Undergraduate standing in Mathematics, Computer Science, Physics, or Engineering (third or fourth year preferred). Strong programming skills in Python are required, along with familiarity with PyTorch or a similar deep learning framework. The student should have completed coursework in ordinary or partial differential equations and basic linear algebra including vector operations, norms, and inner products. Previous exposure to neural networks or machine learning through coursework is an asset but not required. We particularly welcome students comfortable working independently on computational experiments and documenting their results carefully.

Research area: I work with combinatorial objects such as symmetric designs, Hadamard designs, strongly regular graphs, association schemes, quantum information theory, with a concentration on computational methods.

Student roles:
The work starts with a short period of preparation and then problem-solving. The problems posed starts with practice on some known results leading to some open problems. Students are required to help with finding appropriate solutions, writing and executing computer programs such as Python, C or C++.

Skills required:
The research involved, in addition to some (basic) theoretical knowledge, requires skill in computer programming and the running of a large network of computers.

Research area: My specialty involves combining combinatorial, geometric, and computational approaches to study the properties of algebraic and topological structures. In particular, my research combines abstract modeling and experimental approaches to address open problems related to Coxeter groups, polytopes (in particular permutahedra, associahedra, and their applications in quantum physics), triangulations, and simplicial complexes.

Student roles:
The student will actively participate in all stages of the research project, from software development to the analysis of mathematical results. An initial responsibility will be to study the theory underlying exterior shifting and symmetric shifting, and then to contribute to their implementation in SageMath by developing, testing, and documenting high-quality code intended for integration into a software platform used by the international scientific community.

Once the tools are implemented, the student will conduct computational experiments on large families of graphs and simplicial complexes. This will include designing experimental protocols, generating data, automating large-scale computations, and analyzing the results to identify patterns, counterexamples, or new avenues of research.

The project will also include an innovative component related to the use of artificial intelligence. The student will explore how AI agents can assist mathematical research by helping to design experiments, analyze data, detect recurring patterns, and formulate conjectures that can then be validated mathematically or experimentally.

Some of the calculations will be performed on high-performance computing infrastructure. The student will learn how to prepare and submit jobs on supercomputers, manage large-scale computational experiments, and optimize the performance of the programs developed.

Throughout the internship, the student will participate in research meetings, present their progress, contribute to the drafting of technical documentation, and take part in scientific discussions regarding the project’s results. This experience will offer a complete immersion in modern research in computational mathematics, combinatorics, and data science.

Skills required:
The candidate should have a strong undergraduate background in mathematics, computer science, or a related field. A basic knowledge of combinatorics, graph theory, or algebra is desirable. Experience with Python programming is required; familiarity with SageMath, Linux, or scientific computing environments is an asset. The project requires strong analytical and problem-solving skills, as well as a curiosity for research. An interest in artificial intelligence, open-source software, and high-performance computing will be particularly appreciated.

Research area: Applied mathematics, optimization, ordinary differential equations, partial differential equations, dynamical system, computational method; Mathematical modelling, infectious diseases epidemiology, statistical methods for curve fitting, data analysis, health economics .

Student roles:
Student will be guided to build specific models from starch (4 weeks); to use data collection and statistical software to estimate parameter values and model validation (3 weeks); model output explanation and paper wrap-up (4 weeks); oral report within research group (1 week).

Students have freedom to discuss with supervisor on-site during their 12-week stay from the beginning to the end. After the intern, the well-done research work can be published as co-author in peer-reviewed journals as an evidence of success.

Skills required:
Familiar with the basic theory and numerical simulations to ordinary differential equation and partial differential equation; basic knowledge of optimization theory and its applications; basic statistical knowledge and skills to deal with data analysis; to use numerical software such as Matlab, Maple, R, Python etc. Interests on infectious disease modelling and prediction.

Research area: As described on my page https://freakonometrics.github.io/, the themes addressed in the work of students under my supervision are primarily focused on understanding and modeling risks, and actuarial models (or predictive models, more generally). Applications range from modeling climate risks to analyzing discrimination and fairness. The models are primarily mathematical and require a solid foundation in mathematics, statistics, game theory, probability, or quantitative economics.

Student roles:
The student will have the option to:
(1) conduct a scientific literature review on a specific field
(2) work on a theoretical paper related to those issues

Skills required:
As mentioned previously, the student will need to have a strong foundation in mathematics, statistics, game theory, probability, programming, or quantitative economics. The direction of the topic will be tailored to take into account the student's strengths. The student must be able to read scientific literature in English.

Research area: Computer algebra is a relatively recent area in computer science and mathematics, though its roots go back at least forty years ago. Whereas numerical computations are well-established to be efficient in many cases, computer algebra strives to address the different and arguably more difficult problems of providing exact solutions, or solutions parameterized by variables in the input. There has been an enormous amount of applications in computer science, mathematics, as well as in engineering and education. My research focus on efficient algorithms in matrix/tensor and polynomial computations, Groebner bases, automated theorem proving, and their applications.

Student roles:
In my research work, there are a lot of algorithms which have to be implemented in the computer algebra software Maple. I need to use these algorithms to compute and test some hypothesis, show the efficiency of the algorithms and also use them to compare my results with others. During the first three weeks, students will learn some Maple programming skill and necessary mathematical background related to my project. After that, students will start to design/implement/test algorithms, and analysis results. They will work with my current research team including graduate students and undergraduate summer research students. Learning the design and implementation of algorithms will provide high quality training for the students.

Skills required:
Students have already taken some advanced algebra courses. Computer programming skill is preferred but not required.

Research area: My main research interests involve applications of probability to physics and computational methods. Some of the specific techniques and definitions that show up in my work include the mixing times of Markov chains, Monte Carlo methods in computation, random matrices, and dimension reduction. Some recent projects include using mixing time estimates to prove effectiveness of a cryptographic scheme, designing new Markov chain Monte Carlo algorithms for dimension reduction, and purely statistical work on estimation of optimal rankings and orderings.

Student roles:
The student will spend a substantial amount of the project getting "up to speed" on the work. They will then either work to type up the details of the planned proof, or work on associated numerical methods. Ideally the student will be able to contribute their own ideas (especially students with background in algebra that complements my own background), but we will have work to do even if inspiration does not strike.

Skills required:
For the main project, the students require a strong background in mathematics, including linear algebra and either probability/analysis or representation theory (depending on which types of estimates they will work on).

For the applications, a background in mathematics or an interest in developing highly efficient numerical methods packages would be welcome.

Research area: Experimental design is the process of planning studies and investigating efficient methods for collecting data for scientific investigation and is commonly used in industrial, agricultural, biological, pharmaceutical, and manufacturing sciences, etc. The objective of an optimal experimental design is to provide interpretable and accurate inference at minimal costs. My primary research interests concern optimization problems in fractional factorial designs, sequential designs, split-plot designs, block designs, and response surface designs, etc. I develop new design theory, methodology, Bayesian approach, and computational algorithms that can be used to obtain optimal experimental designs.

Student roles:
In my research work, a lot of problems involve the developments of computer programs that are used to search for optimal designs. I also need to compare my results with others. Learning and developing computer programs will provide high quality training for the students. During the first three weeks, students will learn some basic programming skill and necessary theoretical background related to my project. After that, students will start to work on the computer programs and analysis results. They will work with my current research team including PhD and MSc students, as well as possible one or two undergraduate summer research students.

Skills required:
Students have taken some basic mathematics and statistics courses. Experience of using statistical software, such as R, is preferred but not required.

Research area: This research is situated at the intersection of infectious disease epidemiology, public health data science, and environmental health analytics. The broader program focuses on data-driven early warning systems for vector-borne diseases, particularly dengue and other arboviral infections influenced by climate variability, urbanization, human mobility, and international travel. The work integrates epidemiological data, environmental indicators, statistical modelling, and visualization to assess transmission risk and support public health preparedness. A major emphasis is on importation-driven transmission dynamics, ecological receptivity, and the development of interpretable and reproducible analytical frameworks that can inform surveillance and decision-making.

Student roles:
The student will contribute to the development of a pilot analytical workflow for assessing dengue transmission risk in Southern China using publicly available data. Under supervision of Professor Seyed Moghadas, the student will participate in literature synthesis, data collection, exploratory analysis, visualization, and preliminary modelling activities.

During the first phase of the internship, the student will conduct a focused review of dengue early warning studies and summarize commonly used predictors, modelling approaches, and validation strategies. The student will then identify, collect, and organize publicly available datasets related to dengue incidence, meteorological conditions, demographic characteristics, mobility indicators, and urban contextual factors.

The student will assist with data cleaning, integration, and construction of city-week-level analytical datasets using R or Python or Julia. Additional responsibilities will include generating descriptive analyses and visualizations to characterize temporal trends, seasonal patterns, and spatial heterogeneity in dengue risk. The student will also support the development and evaluation of preliminary statistical or transmission-informed models, including regression-based and distributed-lag approaches.

The student will also contribute to interpretation of findings, sensitivity analyses, and preparation of reproducible analytical scripts and visual outputs. At the end of the internship, the student will help prepare a concise research report and presentation summarizing methods, findings, limitations, and future directions. The internship is designed to provide hands-on experience in infectious disease data science, epidemiological analysis, reproducible research workflows, and public health risk assessment within a collaborative international research environment involving York University and Fudan University.

Skills required:
The project is suitable for an undergraduate student with interests in public health, epidemiology, infectious disease modelling, statistics, data science, environmental health, or related fields. Experience with R or Python or Julia is desirable, particularly for data cleaning, visualization, or statistical analysis. Familiarity with epidemiological concepts, modelling, simulations, regression analysis, geospatial data, and reproducible research workflows would be beneficial. Strong analytical thinking, organization, and willingness to work with multidisciplinary datasets are important. The project will provide mentorship and training throughout the internship.

Research area: Mes recherches portent sur la modélisation mathématique et le développement de méthodes numériques pour l'analyse de systèmes non linéaires complexes. Mes domaines d'expertise comprennent l'analyse numérique, la méthode des éléments finis, la continuation numérique et la théorie des bifurcations. J'étudie en particulier les problèmes de mécanique des matériaux en grandes déformations ainsi que les modèles de dynamique des populations. Mes travaux combinent modélisation, analyse mathématique et calcul scientifique afin de concevoir des outils prédictifs robustes pour l'étude de phénomènes physiques et biologiques.

Student roles:
L’étudiant participera au développement et à l’analyse d’un modèle mathématique continu de dynamique de population pour le crabe des neiges, en intégrant explicitement la phase larvaire dans un système d’équations différentielles. Son rôle consistera d’abord à effectuer une revue de littérature ciblée sur les modèles structurés en stades et sur les approches existantes en dynamique des populations pour cette espèce ou des systèmes similaires.
Par la suite, l’étudiant contribuera à la formulation mathématique du modèle, en définissant les équations décrivant les transitions entre les stades larvaires, immatures et matures, ainsi que les paramètres biologiques associés. Il participera à l’identification des hypothèses de modélisation et à la structuration du système dynamique en tenant compte des processus de croissance, de mortalité et de maturation.
L’étudiant sera également impliqué dans l’analyse qualitative du système (points d'équilibre, stabilité). Une attention particulière sera portée à l’identification de structures de type lent-rapide induites par les différences d’échelles de temps entre les stades biologiques.
En parallèle, il développera des outils de simulation numérique afin d’explorer le comportement du modèle sous différentes conditions environnementales. Cela inclura l’implémentation de méthodes numériques appropriées (par exemple en MATLAB), ainsi que l’analyse des résultats obtenus.
L’étudiant bénéficiera d’un encadrement étroit tout au long du projet, avec des rencontres régulières permettant un suivi continu de l’avancement, des discussions scientifiques approfondies et des ajustements méthodologiques au besoin. Ce suivi rapproché favorisera son apprentissage progressif et son autonomie en recherche.
Finalement, l’étudiant participera à l’interprétation biologique des résultats et à la communication scientifique des conclusions, sous forme de rapports techniques ou de présentations. Ce rôle lui permettra d’acquérir une expérience intégrée en modélisation mathématique, analyse des systèmes dynamiques et calcul scientifique appliqué à un problème biologique concret.

Skills required:
Un étudiant de niveau baccalauréat ayant une bonne formation en mathématiques appliquées, notamment en équations différentielles, calcul scientifique et modélisation mathématique, est recherché pour ce projet. Des notions de base en analyse numérique et en programmation scientifique (MATLAB ou équivalent) sont souhaitées, sans être obligatoires à un niveau avancé. L’étudiant doit démontrer de la curiosité pour les applications des mathématiques en biologie et en dynamique des populations, ainsi qu’une capacité à comprendre et manipuler des modèles mathématiques. Un intérêt pour les systèmes dynamiques et la simulation numérique constituera un atout important pour ce projet de recherche interdisciplinaire.

Research area: My research focuses on operations research, optimization, game theory, and healthcare systems. I develop mathematical and computational models to study decision-making problems involving pricing, procurement, competition, and resource allocation. My work examines how institutional rules and incentives influence the behavior of organizations and market participants. By combining analytical modeling, optimization, simulation, and quantitative analysis, I aim to generate insights that support more effective healthcare policies and improve access to essential services and products.

Student roles:
The student will be actively involved in all major stages of this research project, which focuses on procurement systems and supplier decision-making in pharmaceutical markets.

**Literature Review:**
The student will review academic articles, policy reports, and industry publications related to procurement systems, supply chains, healthcare markets, and supplier incentives. They will summarize key findings and identify important research questions.

**Model Development:**
The student will assist in developing mathematical and computational models that describe interactions between procurement organizations and suppliers. These models will be used to study how different procurement rules affect prices, supplier participation, and supply reliability.

**Computational Analysis:**
The student will conduct numerical experiments and simulation studies to evaluate alternative procurement policies and market scenarios. They will analyze how model assumptions influence outcomes and identify key factors affecting performance.

**Result Interpretation:**
The student will help interpret model results and examine their practical implications for healthcare systems and procurement policy.

**Research Communication:**
The student will assist in preparing reports, figures, summaries, and presentations describing the methods and findings of the project.

Through this project, the student will gain experience in mathematical modeling, optimization, simulation, analytical thinking, and scientific communication while contributing to research with important implications for healthcare systems and public policy.

Skills required:
The student should have a background in mathematics, operations research, industrial engineering, economics, statistics, computer science, analytics, or a related field. Familiarity with calculus, probability, optimization, mathematical modeling, or programming is desirable. Experience with Python, MATLAB, R, Mathematica, or similar software would be beneficial but is not required. Strong analytical thinking, problem-solving ability, and curiosity about real-world decision-making problems are important. Students interested in optimization, game theory, simulation, or healthcare applications are particularly encouraged to apply.

Research area: My research primarily focusses on using techniques from probability theory to better understand various objects arising in statistical mechanics and mathematical physics. These days, most of my research time is spent in understanding certain random trees, random height models and disordered models.

Student roles:
The student will read some of the papers, try to gather some feel of the general area, and attack some of the closely related toy open problems.

Skills required:
Good exposure to probability theory, and general inclination towards graph theoretic problems is desired (but no graph theory knowledge is required)

Research area: I am a numerical analyst working in the areas of scientific computing and mathematical modelling. In particular, I am interested in parallel and adaptive numerical techniques for the approximation of partial differential equations. I also work on large scale optimization problems of interest to industry.

Student roles:
Depending on interest and skill set the student could be involved in both the mathematical theory and computation, or spend most of their time on one or the other. They will be active participants in the writing of the associated papers.

Skills required:
A course in numerical methods is required, a course in numerical methods for PDEs is preferred but not necessary. The intern should have some python programming experience. Experience with technical writing using LaTeX is also preferred.

Research area: Number theory, Graph Theory

Student roles:
Read research papers, carry out mathematical proofs and write a report on new findings.

Skills required:
Knowledge in number theory, graph theory, some programming experience with mathematical softwares.

Research area: My specialized research area focuses on the intersection of reliability and maintenance, human activity recognition, planning and scheduling, operations research (both deterministic and stochastic) and machine learning and artificial intelligence. I explore the application of advanced mathematical programming, machine learning techniques and AI algorithms to enhance the reliability and maintenance processes in various industries. This involves developing models and algorithms for human activity recognition to understand patterns and behaviors that impact system reliability. Additionally, I investigate optimization techniques based on deterministic and stochastic operations research to improve planning and scheduling of maintenance activities, maximizing resource utilization, and minimizing downtime.

Student roles:
The role of the student will involve various tasks and responsibilities.
1. Familiarization and literature review: Initially, the student will study relevant literature, research
papers, and existing approaches to gain a comprehensive understanding of the problem and its
intricacies.
2. Problem Refinement: The student will work closely with the project advisor to refine the problem
formulation and define the specific requirements and constraints to be considered in the research
project.
3. Mathematical Model Development: Based on the problem refinement, the student will develop a
mathematical optimization model that captures formulate the problem, considering factors such as
technician skills, time windows, travel distances, and any additional constraints.
4. Algorithm Design and Implementation: The student will design/improve efficient algorithms to
solve the formulated optimization model. The algorithms will be implemented using programming
languages such as Python, Java, or C++, considering data structures and optimization libraries as
needed.
5. Experimentation and Evaluation: The student will conduct experiments to evaluate the
performance and effectiveness of the developed algorithms. The student will analyze and interpret
the results obtained from the experiments.
6. Algorithm Refinement and Optimization: Based on the evaluation results, the student will refine
and optimize the algorithms to improve their performance.
7. Documentation and Reporting: Throughout the research project, the student will maintain clear
and organized documentation of the work performed. At the end of the project, the student will
prepare a final research report that presents the problem, methodology, results, and conclusions of
the research.

Skills required:
To work on the research project, the student should have a strong foundation in operations
research, optimization, and algorithm design. They should possess the following skills and
background:
1. Mathematics, Modeling and Operations Research: A solid understanding of mathematical
optimization techniques, including linear programming, and integer programming is needed.
2. Algorithm Design and Analysis: The student should have experience in designing algorithms and
evaluating their efficiency and performance. Knowledge of heuristic and metaheuristic techniques
commonly used in solving optimization problems, such as genetic algorithms, simulated annealing,
3. Communication and Collaboration: Effective communication skills are important to present
research findings

Research area: I study subspaces of C*-algebras. Such algebras serve as abstract foundations for quantum physics. A fundamental postulate requires them to be unchanged under a natural symmetry operation. In practice, physical problems are often analyzed through perturbations, whereby the rigid structure of C*-algebras is compromised. My research provides a theory of these perturbed structures, and exhibits new ways of recovering the lost symmetry. Recently, I am applying these ideas to construct mathematically rigorous models in quantum field theory, via the Wightman axioms, the Haag-Kastler axioms (and their perturbative counterparts), or via Rieffel's notion of strict quantization.

Student roles:
The first step will be a guided exploration of some of the existing literature to precisely assess what is known for the so-called free scalar field. The student will need to acquire a good understand of the construction of the various QFT models in this concrete yet non-trivial case, as a stepping-stone to eventually tackle some interacting fields.

On a day-to-day basis, the student will analyze examples and calculations in detail, as well as try to solve sub-problems, based on my guidance. Once a week, I will hold a one-on-one meeting with the student to discuss their questions, ideas, attempts and progress. Working together, we will formulate conjectures and prove theorems towards a solution of the problems listed in the research project. This could lead to a joint publication.

We will also hold a weekly seminar where the student will present the material from the literature to my research group of undergraduate students, graduate students, and postdoctoral fellow.

Skills required:
Knowledge of basic real and complex analysis and of linear algebra is required. Familiarity with abstract algebra (groups, rings, modules), functional analysis and quantum mechanics is a desirable asset, but is not strictly required. The precise direction of this project is somehow flexible, and depending on your mathematical background and interests, the project could have an analytic flavour, an algebraic flavour, or even a mix of the two.

Research area: My research interests revolve around smart radio environment with more emphasis on (i) interpretable machine learning for communication network, (ii) intelligent reconfigurable surfaces (IRS) aided communication and (iii) embedded AI for low power internet of things. My research projects tackle the open issues on using different learning approaches in combination with different optimization techniques for efficient and interpretable end-to-end communication learning, and shade light on real time beamforming and IRS control with constraints dictated by the channel estimation overhead. Herein, machine learning is also considered as a potential enabler in realising the vision of IRS- empowered smart radio environment.

Student roles:
The first project aims at exploring the learning methods, optimization techniques and network architectures space. So far, backpropagation and gradient descent (GD) are the most dominant learning and optimization techniques respectively. Therefore, the student will survey and explore other learning and optimization approaches that will not necessarily rely on backpropagation and gradient descent techniques. The student shall consider data-driven approach with expert knowledge architecture and model-based approach where deep unfolding technique is used. For end-to-end communication learning, the focus is on the design of an efficient end-to-end communication system learning approach based on the optimal use of data-driven and model-based approaches. Optimality is measured in terms of both system performance and computational complexity (including training speed).
The second project’s objective is to provide a unified theoretical foundation and framework to interpret and understand the performances of the models proposed in project #1 and investigate the effect of model inaccuracy and dimensioning. Performing a theoretical analysis for model-based learning (be it data-driven with expert knowledge or model-based via deep unfolding) seems feasible, but not necessarily straightforward, even if the algorithms are based on some specific models that always yield rigorous analytical results within certain performance bound.Finally, in the third project, the student is called to participate on developing a proof of concept that enables Sionna (a TensorFlow-based open-source library for simulating the physical layer of wireless communication systems) on top of a Radio Frequency System On Chip (A system-on-chip (SoC) for communications that contains multiple radio frequency (RF) components).
Basically, with the collaboration of PhD and masters' students, the qualified interns will mainly contribute to project 1 and 3.

Skills required:
1. Good theoretical background in communication theory
2. Good linear algebra and optimization theory
3. Good skills in Python and Matlab
4. Intermediate level in scikit-learn and Keras frameworks
5. Familiar with DL library Sionna from NVIDIA

Research area: Computer communications and networks, particularly protocol design, performance analysis and applied network security.

Student roles:
The intern student will work with faculty members and graduate students, learning through the research process and helping with simulation and evaluation, which will lead to publishable work with technology transfer potentials.

For more information about the research projects, the related projects and the experience of the former MITACS interns, please refer to http://web.uvic.ca/~pan and the references therein.

[1] Y. Zhuang, J. Pan, and L. Cai, “Minimizing energy consumption with probabilistic distance models in wireless sensor networks”, in Proc. 29th IEEE International Conference on Computer Communications (INFOCOM’10), pp. 2453–2461, 2010.

[2] Y. Zhuang, Y. Luo, L. Cai, and J. Pan, “A geometric probability model for capacity analysis and interference estimation in wireless mobile cellular systems”, in Proc. 54th Global Telecommunications Conference (GLOBECOM’11), 2011.

[3] Liang He, Zhe Yang, Jianping Pan, Lin Cai, and Jingdong Xu, "Evaluating Service Disciplines for Mobile Elements in Wireless Ad Hoc Sensor Networks", in Proc. 31st IEEE International Conference on Computer Communications (INFOCOM'12), Orlando, USA, 2012.

[4] Liang He, Yu Gu, Jianping Pan, and Ting Zhu, "On-Demand Charging in Wireless Sensor Networks: Theories and Applications", in Proc. 10th IEEE International Conference on Mobile Ad-hoc and Sensor Systems (MASS'13), Hangzhou, China, October, 2013.

[5] M. Ahmadi and J. Pan, “Random distances associated with arbitrary triangles: A recursive approach with an arbitrary reference point,” Available Online: http://dl.handle.net/1828/5134, 2014.

[6] F. Tong, M. Ahmadi, and J. Pan,“Random Distances Associated with Arbitrary Triangles: A Systematic Approach between Two Random Points,” arXiv:1312.2498, 2013.

[7] F. Tong and J. Pan, "Random Distances Associated with Arbitrary Polygons: An Algorithmic Approach between Two Random Points," arXiv:1602.03407, 2016.

[8] R. Pure, S. Durrani, F. Tong, and J. Pan, "Distance Distribution Between Two Random Nodes in Arbitrary Polygons," arXiv:1903.07757, 2019.

Skills required:
The MITACS intern student is expected to be familiar with the basics of wireless communications and networking. Wireless communication background is needed to better understand how the signal attenuates, and how to model it through appropriate distance distribution models.

Research area: My research lies at the intersection of mathematical optimisation, machine learning and mathematical modelling (in particular using probability theory).

Student roles:
The student will experiment with data, train and implement the machine learning models and implement the fairness audit. If the project progresses as planned, the work will contribute to a research article to be co-authored by the student.

The project will take place at UQAM, the Centre de recherche mathématiques (CRM) and the Group d'études et de recherche en analyse de décision (GERAD). The student will be able to participate in scientific activities in this rich environment.

Skills required:
Required: basic familiarity with optimisation models

Required: a good understanding of algorithmic thinking and strong knowledge of at least one programming language, preferably Python or C.

Exposure to supervised machine learning (at the level of an introductory course) is highly desirable.

Research area: Part of my research involves formalized mathematics and formalized computing, which is done using a proof assistant. I am most interested in building large libraries of computational knowledge, and the techniques necessary to reach large scale.

Student roles:
Implement various domains of mathematics and computer science in Agda. While the domains will be drawn from known areas, the implementations will be new, and often require novel ideas too. Some creativity (with guidance) will be needed to find good encodings of certain concepts. Looking at the current library is the best way to understand the kinds of computing and mathematics involved. But also looking at the libraries of other systems (Isabelle, Coq, Lean, Idris, etc) is also a good guide.

Skills required:
Experience programming in at least 2 programming languages, but more is better. Some functional language (such as Haskell) would be optimal. A solid background in Mathematics. Must like doing things very precisely.

Research area: I have been working on supply chain issues mainly relevant to contract design under uncertainty, pricing and revenue management, and gray markets. I use game theory and optimization techniques in my research. More recently, I have studied government interventions in pharmaceutical industries to improve affordability. My current research investigates how to create transparency in markets with quality differentiation. Another ongoing area of my research focuses on the adaptation of an agentic AI system for measuring supply chain emissions. The proposed idea in this research aligns well with my previous studies regarding policy design to support sustainable AI technologies.

Student roles:
The student’s role has three phases.
• Phase 1-Problem definition (weeks 1-4): The student will review relevant reports and data bases to collect information about the benefits and challenges of AI systems in the energy sector. The student will also research regulations or policies that can be used to support energy efficiency in AI systems. The student will prepare a list of 4-5 major policies recommended or applied by different organization (e.g., United Nations) or countries (e.g., Canada). The information collected will help define a clear research question based on real-world evidence.
• Phase 2-Literature Review (weeks 5-8): The student will conduct a major literature review of this topic by exploring scientific journals and databases. The review will provide insight into how our research will contribute to the existing literature.
• Phase 3-Modeling and Analysis (weeks 9-12): The student will learn Mathematica as a modeling software. I will help them develop a game theory model to analyze strategic decisions of government agencies and AI companies in Mathematica. The analytical model will be developed based on our search results in phases 1 and 2. The student will learn how to use optimization models to analyse decisions in an AI supply chain with different economic and environmental objectives and constraints. The student will have frequent in person meetings with me (1-2 hours per week) and will provide clear and timely updates regarding their progress in each phase.
I will keep this plan flexible. If time permits, the student will be included in the development of a paper to be presented in a peer reviewed conference or journal. I will also connect the student to professional development events and social activities occurring at Memorial University and the beautiful city of St. John’s.

Skills required:
The student should have a background in Business or Management disciplines with a focus on Operations Management or Supply Chain Management. The research may also be of interest to students with a background in Industrial Engineering, Applied Math, or Economics.
The student is expected to be well organized and highly interested in the proposed research project. The student should have strong written and verbal communication skills and excellent time management skills.

Research area: My research lies at the intersection between discrete mathematics and biosciences. More specifically, my research seeks to provide insights into biomolecular interactions using tools from combinatorics and graph theory. One central theme concerns structural problems in graph theory that are motivated by DNA self-assembly processes (which are methods to synthesize nanostructures using building blocks made of DNA). Of interest is determining optimal design strategies to build a target complex modeled as a graph. To this end, I focus on studying two new graph parameters for various classes of graphs under different design constraints.

Student roles:
During the first couple of weeks, the student will read some published works to gain familiarity with the research topic, notation, and methodology used. Then, the student will apply those tools to selected examples and open questions, not yet analyzed. The goal is to find the minimum number of molecules and of bonds needed to build a given target graph. Whenever the exact values cannot be found, the student will determine upper and lower bounds for these two parameters. This research work may include developing new strategies for obtaining such values or bounds. When computing these parameters, the student will be focusing on certain scenarios treated in the literature. During this internship, the student will write weekly reports (using LaTeX, for instance) to summarize their findings and challenges faced. In fact, the student is expected to meet regularly (e.g. once per week) with their supervisor to discuss progresses and future developments.

Skills required:
The student needs to be familiar with basic notions in graph theory, such as edge-colorings and vertex-colorings, directed graphs, Eulerian graphs, cycles, bipartite graphs, etc. The student also needs basic knowledge in linear algebra; this includes matrix algebra and being able to solve a system of linear equations. Some background in computer programming may be helpful. Familiarity with LaTeX is an asset but it is not required since guidance will be provided.

Research area: My interests are in the areas of algebraic number theory, especially on algebraic lattices (ideal lattices, log unit lattices of number fields, Gross lattices, ...), elliptic curve isogenies, and their applications in post-quantum cryptography and coding theory.

Student roles:
The students will first study the background on ideal lattices of number fields (2–3 weeks), then run experiments in SageMath or Pari/GP to compute ideal lattices and their shapes (2 weeks). After that, they will gather the data, analyze it, form conjectures based on the properties of ideal lattice shapes, and attempt to prove them (4–5 weeks in total). In the final 2 weeks, they will study isogeny-based cryptography and how to apply the results concerning the shapes of ideal lattices to analyze the efficiency and security of these cryptosystems.

Both students will work together at every stage of the project.

Skills required:
Students should have background in basic algebra (linear algebra and abstract algebra). Having some knowledge on quadratic fields, lattices and some programing experience are preferable.

Research area: My research focuses on the development of optimization and artificial intelligence methods to enhance the reliability, availability, and resilience of complex engineering systems. Current research areas include selective maintenance optimization, predictive maintenance, mission-abort policies, and the resilience of critical infrastructure networks. This research integrates mathematical modeling, stochastic processes, machine learning, and optimization techniques to support maintenance and operational decision-making. Applications include aerospace systems, transportation networks, autonomous systems, production systems, and other safety-critical engineering systems where reliability, safety, and operational performance are of paramount importance.

Student roles:
The student will contribute to the development of reliability and optimization models for balanced mission-oriented systems. Initially, the student will familiarize themselves with the concepts of selective maintenance and balanced systems using key papers, notes, and guidance provided by the supervisors. Working closely with the supervisors, the student will assist in the formulation of a selective maintenance optimization model for balanced systems and the development of supporting reliability and degradation models. The student will implement solution approaches in Python, building upon existing code developed by the research team for related maintenance optimization problems. The student will conduct computational experiments and sensitivity analyses to evaluate model performance and gain experience in optimization and reliability engineering. Finally, the student will prepare a short conference-style report summarizing the methodology and results.

Skills required:
The ideal candidate will have a background in operations research, industrial engineering, applied mathematics, computer science, or a related discipline. Familiarity with mathematical modeling, optimization, probability, and statistics is desirable. Experience with programming, particularly in Python, is considered an asset. Exposure to topics such as machine learning, reliability engineering, simulation, or optimization software is beneficial but not required. Most importantly, we are seeking a motivated and curious student with strong analytical skills, a willingness to learn, and an interest in applying mathematical and computational methods to real-world engineering problems.

Research area: Our lab specializes in mathematical epidemiology and computational modelling of infectious disease dynamics. We combine classical compartmental models such as SEIR with modern machine learning techniques, particularly physics-informed neural networks, to analyze disease outbreaks when surveillance data is noisy, sparse, or incomplete. A core interest is inverse problems, where unknown epidemiological parameters such as transmission rate, incubation period, and recovery rate must be estimated from observed infection data. This work sits at the intersection of applied mathematics, public health, and deep learning, and aims to produce tools useful for real-time epidemic forecasting and policy decisions.

Student roles:
The intern will work as a research contributor within the DIMMS Lab on a focused computational project at the intersection of mathematical epidemiology and deep learning. During the first two weeks, the intern will onboard by studying our published work on SEIR-based PINNs, reading introductory material on inverse problems in epidemiology, and running our existing forward-problem codebase to understand the baseline training procedure. By the end of week two, the intern should understand the SEIR model and be able to reproduce a standard forward simulation. From weeks three to seven, the intern will modify the PINN architecture to treat the epidemiological parameters as learnable quantities. This involves adding new trainable scalars to the model, redefining the loss function to support joint parameter estimation, and integrating our adaptive gradient method. The intern will develop a test suite using synthetic ground-truth data with known parameters across multiple noise levels. From weeks eight to ten, the intern will systematically evaluate parameter recovery accuracy. This includes running experiments across varied noise levels, sparsity levels, and initialization strategies, producing comparison tables, and diagnosing any failure modes encountered. Weekly meetings with the supervising faculty and PhD student will guide the experimental direction. During weeks eleven and twelve, the intern will write up the results, produce publication-quality figures, and present findings to the DIMMS Lab in a final seminar. The intern will also draft the methods and results sections of a potential journal submission. The intern will be expected to work independently on coding tasks, document experiments carefully, and communicate results clearly. We will provide all computing resources including GPU access, full supervisory support through weekly meetings, and access to the lab's ongoing research discussions.

Skills required:
Undergraduate standing in Mathematics, Statistics, Computer Science, Physics, or a related quantitative discipline (third or fourth year preferred). Programming experience in Python is required along with familiarity with PyTorch or TensorFlow. The student must have completed coursework in ordinary differential equations and should be comfortable with basic optimization concepts. Interest in mathematical biology, epidemiology, or public health modelling is strongly preferred. Prior exposure to inverse problems or parameter estimation is an asset but not required. We welcome students who are curious about applying mathematical methods to real-world biological and epidemiological questions.

Research area: Number theory, Algebra

Student roles:
Read research papers, carry out mathematical proofs and write a report on new findings.

Skills required:
Knowledge in Number theory, Algebra, some programming experience with mathematical softwares.

Research area: My research focuses on the development of optimization and artificial intelligence methods to enhance the reliability, availability, and resilience of complex engineering systems. Current research areas include selective maintenance optimization, predictive maintenance, mission-abort policies, and the resilience of critical infrastructure networks. This research integrates mathematical modeling, stochastic processes, machine learning, and optimization techniques to support maintenance and operational decision-making. Applications include aerospace systems, transportation networks, autonomous systems, production systems, and other safety-critical engineering systems where reliability, safety, and operational performance are of paramount importance.

Student roles:
The student will contribute to the development of optimization and machine learning models for UAV routing and mission-abort decision-making in uncertain environments. Initially, the student will familiarize themselves with the relevant literature on UAV routing and mission-abort policies using key papers, notes, and guidance provided by the supervisors. Working closely with the supervisors, the student will assist in the formulation of routing and mission-abort decision models that account for random shocks and operational uncertainty. The student will implement optimization and learning-based solution approaches in Python and evaluate their performance through computational experiments. Existing code developed by the research team for UAV routing and mission-abort optimization will be provided as a starting point. The student will conduct sensitivity analyses to assess the impact of key model parameters and compare alternative decision-making approaches. Finally, the student will prepare a short conference-style report summarizing the methodology, computational results, and key research findings.

Skills required:
The ideal candidate will have a background in operations research, industrial engineering, applied mathematics, computer science, or a related discipline. Familiarity with mathematical modeling, optimization, probability, and statistics is desirable. Experience with programming, particularly in Python, is considered an asset. Exposure to topics such as machine learning, reliability engineering, simulation, or optimization software is beneficial but not required. Most importantly, we are seeking a motivated and curious student with strong analytical skills, a willingness to learn, and an interest in applying mathematical and computational methods to real-world engineering problems.

Research area: My specialized research area is community-oriented artificial intelligence, mathematical modeling, and data science for infectious disease prevention, preparedness, and response. I develop AI-enabled and mathematical modeling approaches to support public-health decision-making, with emphasis on epidemic dynamics, behavioral responses, vaccination strategies, climate and environmental drivers, and health equity. This research integrates epidemiological data, climate-informed modelling, and community-relevant analytics to address infectious disease challenges in Canada, Africa, and the Global South, while supporting resilient health systems and equitable outbreak response.

Student roles:
The student will review literature on category theory, multimodal learning, and data fusion, then help develop a mathematical framework that represents data modalities as objects and relationships or transformations as morphisms. They will formulate theoretical structures, design algorithmic prototypes, and test the framework using real-world multimodal fusion tasks. The student will also analyze results, prepare visualizations, document methods, and contribute to manuscript writing. Regular meetings with supervisors and interdisciplinary collaboration will be expected throughout the project.

Skills required:
The ideal student should have a background in mathematics, applied mathematics, computer science, data science, artificial intelligence, machine learning, statistics, or a related field. Familiarity with abstract algebra, category theory, linear algebra, probability, machine learning, and multimodal data analysis is preferred. Experience with programming in Python, R, Julia, or MATLAB, and with machine-learning libraries would be an asset. The student should have strong mathematical reasoning, analytical, coding, writing, and communication skills.

Research area: I have a background in physics and chemistry and work in the field of plasma physics, notably for CO2 capture and conversion into added-value chemicals using plasmas.

Student roles:
The student will lead the project and conduct the literature search and develop a first simple analytical and/or numerical model using computational tools.

Skills required:
The student should have a background in physics or mathematics and an interest in solving applied mathematics problems.

Research area: My research primarily focusses on using techniques from probability theory to better understand various objects arising in statistical mechanics and mathematical physics. These days, most of my research time is spent in understanding certain random trees, random height models and disordered models.

Student roles:
--Understand the basics of the project, and read our paper to gain some basic knowledge about the problem.
--Use the recursive distributional equation to code the outcomes of the iteration. This involves plugging in various different boundary conditions, and analyzing the outcomes. Then try to use theory to explain these outcomes, make conjectures, gain insights, and then try to prove some of the conjectures. Usually the simulations help in finding the right bounds to use to prove these conjectures.
--The goal is to provide a fulfilling research experience where the student can discover something new through the code, and then try to prove them mathematically using some of the theory developed by me and co-authors.

Skills required:
My research involves a good mix of probability theory, analysis and combinatorics, so proficiency in these areas are desired (but not essential.)
This particular project requires some basic coding skills (e.g. Python).
Some basic proof writing skills is desired.

Research area: My research area is quantum information science, fault-tolerant quantum computing, and the design of error-correcting codes that reduce the overhead of reliable quantum computation. I am particularly interested in stabilizer codes, CSS codes, logical gate implementation, circuit compilation, and resource-efficient architectures for near- and medium-term quantum hardware. This work connects quantum coding theory with practical simulation, optimization, and systems-level design, aiming to identify when new code families can outperform conventional approaches such as surface codes in realistic computational settings.

Student roles:
The student will work as a junior researcher on the theory-to-prototype pipeline for phantom quantum codes. In the first phase, the student will study background material on stabilizer codes, CSS codes, logical qubits, logical operators, and fault-tolerant entangling gates. They will prepare a concise internal summary explaining what makes phantom codes different from conventional stabilizer-code approaches and why avoiding physical entangling gates could reduce overhead.

In the second phase, the student will implement basic computational tools for working with CSS stabilizer codes. These may include binary matrix representations, commutation checks, logical-operator extraction, code-distance calculations for small examples, and visualization of stabilizer or logical-operator structure. The student will use these tools to reproduce simple examples and develop intuition for intrinsic encoded entanglement.

In the third phase, the student will pursue one focused research direction. Possible options include enumerating small candidate codes, experimenting with SAT-based search formulations, classifying logical operations available within a code, simulating simple encoded circuits, or comparing toy resource estimates against surface-code-style implementations. The exact direction will be matched to the student’s background and interests.

In the final phase, the student will consolidate their results into polished research artifacts: documented prototype code, a technical report, clear diagrams, and a final presentation for both quantum-information and systems-oriented audiences. The student will participate in weekly meetings, present progress, discuss obstacles, and receive mentorship on research methods, paper reading, mathematical writing, and scientific communication.

This project is especially suited for an ambitious undergraduate considering graduate study in quantum computing, theoretical computer science, physics, applied mathematics, or cryptography-adjacent quantum information.

Skills required:
The student should have strong preparation in linear algebra, discrete mathematics, algorithms, and probability. Prior exposure to quantum computing, stabilizer codes, error correction, Boolean satisfiability, or graph theory is helpful but not required. Programming experience in Python is strongly recommended; familiarity with NumPy, linear algebra over finite fields, simulation, or optimization libraries would be valuable. The ideal student is mathematically mature, comfortable learning from research papers, careful with definitions, and excited by problems at the intersection of quantum theory, coding, algorithms, and computational experimentation.

Research area: My research is in theoretical cosmology and mathematical physics. I study fundamental questions about the origin, evolution, and large-scale structure of the Universe, with research spanning the Big Bang, cosmic inflation, dark energy, and gravitational-wave cosmology. More recently, I have focused on understanding the connection between the large-scale distribution of matter and astrophysical tracers, developing theoretical and computational frameworks that combine cosmological simulations, galaxy formation models, and gravitational-wave source populations to probe dark matter and cosmic structure.

Student roles:
Students will begin by learning the scientific background of the project through guided reading of introductory literature on cosmology, gravitational-wave astronomy, and binary black hole formation, as well as the computational tools and programming skills needed for the project, including basic data-analysis techniques.
After this initial training, students will work on a research problem related to modeling binary black hole populations and their connection to galaxies and dark matter. Depending on the project direction, tasks may include analyzing simulation and observational data, implementing and testing theoretical models, performing statistical analyses, and visualizing results. Students will participate in regular meetings with the supervisor and her research group, present their progress, and contribute to the interpretation and communication of research findings. In addition to being hosted in the Department of Applied Mathematics at the University of Waterloo, students will engage with researchers at Perimeter Institute, where they will have opportunities to participate in cosmology seminars, workshops, and other scientific activities while benefiting from its vibrant research environment.

Skills required:
Students should have a strong interest in physics, astronomy, mathematics, or related fields. Familiarity with undergraduate-level calculus, classical mechanics, statistics, and basic programming (preferably Python) is desirable. Prior coursework in astrophysics, cosmology, data analysis, or computational physics would be beneficial but is not required. The project is suitable for motivated students with strong quantitative and problem-solving skills who are interested in learning scientific computing and exploring modern topics in cosmology, gravitational-wave astronomy, and astrophysics.

Research area: My specialized research area is community-oriented artificial intelligence, mathematical modeling, and data science for infectious disease prevention, preparedness, and response. I develop AI-enabled and mathematical modeling approaches to support public health decision-making, with an emphasis on epidemic dynamics, behavioral responses, vaccination strategies, climate and environmental drivers, and health equity. This research integrates epidemiological data, climate-informed modelling, and community-relevant analytics to address infectious disease challenges in Canada, Africa, and the Global South, while supporting resilient health systems and equitable outbreak response.

Student roles:
(1) The student will develop and analyze a mathematical model of malaria transmission that incorporates human behavior, vaccination strategies, climate velocity, and seasonal mosquito biting rates. (2) They will construct systems of differential equations, run simulations, and interpret results to understand the dynamics of malaria spread. (3) The student will also source and integrate relevant epidemiological and climate data from open-access repositories such as https://acadic.org/africa-in-data/. (4) They will prepare visualizations and contribute to academic writing and presentations. (5) The role requires independent initiative, regular collaboration with supervisors, and potential engagement with international research partners across the Global South.

Skills required:
(1) The ideal student will have a strong background in mathematical modeling, particularly in infectious disease dynamics and differential equations. (2) Experience with compartmental models (e.g., SIR/SEIR), and proficiency in simulation tools such as MATLAB, Python, or R is essential. (3) Familiarity with epidemiological concepts, vaccination strategies, and environmental drivers like climate velocity is preferred. (4) The student should be capable of analyzing seasonal variations and integrating real-world data from sources such as https://acadic.org/africa-in-data/. (5) Strong analytical and communication skills and the ability to work independently and collaboratively in interdisciplinary and cross-cultural research environments are required.

Research area: My specialized research area is community-oriented artificial intelligence, mathematical modeling, and data science for infectious disease prevention, preparedness, and response. I develop AI-enabled and mathematical modeling approaches to support public-health decision-making, with emphasis on epidemic dynamics, behavioral responses, vaccination strategies, climate and environmental drivers, and health equity. This research integrates epidemiological data, climate-informed modelling, and community-relevant analytics to address infectious disease challenges in Canada, Africa, and the Global South, while supporting resilient health systems and equitable outbreak response.

Student roles:
The student will develop and analyze mathematical models of measles transmission in Canada, focusing on immunity gaps, imported cases, under-vaccinated clusters, and targeted catch-up vaccination strategies. They will review relevant literature, source and organize epidemiological and vaccination data, formulate model equations, run simulations, evaluate outbreak-risk scenarios, and interpret results for public-health planning. The student will prepare figures, contribute to presentations and manuscript writing, and meet regularly with supervisors and interdisciplinary collaborators.

Skills required:
The ideal student should have a background in mathematics, applied mathematics, epidemiology, public health, biostatistics, statistics, data science, computational biology, or a related field. Familiarity with infectious disease modeling, compartmental models, vaccination dynamics, outbreak analysis, and numerical simulation is preferred. Experience with Python, R, MATLAB, Julia, or similar tools would be an asset. Strong analytical, mathematical reasoning, coding, writing, and communication skills are required.

Research area: My research focuses on mathematical modeling and analysis of cancer immunotherapy and cellular signaling pathways. I develop various types of mathematical models to mimic the dynamics and interactions in the tumor microenvironment (TME) under different cancer therapies or to address specific biological questions. My modeling work involves both qualitative and quantitative studies. In cancer studies, we use model predictions to evaluate potential treatment strategies, aiming to design optimal personalized treatment protocols or identify biomarkers for therapies. For cellular signaling pathways, our works help filter hypotheses and identify unknown factors, and predict the behavior of mutations under specific stimuli.

Student roles:
1. Read and present the related experimental and/or modeling papers
2. Create mathematical models: PDE models (fixed or free boundary) or ODE models
3. Find experimental evidence to support the assumption of the models
4. Write the Matlab codes to generate the numerical solution for the created models
5. Perform the model calibration for data fitting
6. Numerical simulation
i) Model validation to the experimental data
Use the Matlab coding to generate accurate numerical solution and adjust the parameter values based on the experimental data, numerical outcome to provide the qualitative fitting. After having this result, the intern needs to explain the finding from the simulation in the Latex file and also create the high-resolution pdf files for these numerical results.
ii) Numerical prediction- synergy analysis / treatment protocol design
test different combinations of treatment dosages and schedule to generate a heat map for this synergy analysis.
iii) Sensitivity analysis
Use the Latin hypercube sampling to generate at least 10000 samples and then calculate their partial rank correlation coefficients (PRCCs) and p-value corresponding to the tumor outcome.
7. Bifurcation analysis
8. Analyze the dynamics of the model
9. Use Latex to write the manuscript for this project

Skills required:
1. Programming skills for Matlab
2. Modeling skills for ODE or PDE models
3. Know how to generate numerical solutions for ODE or PDE model by using Matlab
4. Willing to learn some biological data / background
5. Analysis skills for ODE model, including existence, uniqueness, and boundedness of solution, positive invariant set, local stability of equilibria, bifurcation analysis
6. Use Latex for manuscript editing

Research area: My research focuses on mathematical modeling and analysis of cancer immunotherapy and cellular signaling pathways. I develop various types of mathematical models to mimic the dynamics and interactions in the tumor microenvironment (TME) under different cancer therapies or to address specific biological questions. My modeling work involves both qualitative and quantitative studies. In cancer studies, we use model predictions to evaluate potential treatment strategies, aiming to design optimal personalized treatment protocols or identify biomarkers for therapies. For cellular signaling pathways, our works help filter hypotheses and identify unknown factors, and predict the behavior of mutations under specific stimuli.

Student roles:
Read and present the related experimental and/or modeling papers
2. Create mathematical models: PDE models (fixed or free boundary) or ODE models
3. Find experimental evidence to support the assumption of the models
4. Write the Matlab codes to generate the numerical solution for the created models
5. Perform the model calibration for data fitting
6. Numerical simulation
i) Model validation to the experimental data
Use the Matlab coding to generate accurate numerical solution and adjust the parameter values based on the experimental data, numerical outcome to provide the qualitative fitting. After having this result, the intern needs to explain the finding from the simulation in the Latex file and also create the high-resolution pdf files for these numerical results.
ii) Numerical prediction- synergy analysis / treatment protocol design
test different combinations of treatment dosages and schedule to generate a heat map for this synergy analysis.
iii) Sensitivity analysis
Use the Latin hypercube sampling to generate at least 10000 samples and then calculate their partial rank correlation coefficients (PRCCs) and p-value corresponding to the tumor outcome.
7. Bifurcation analysis
8. Analyze the dynamics of the model
9. Use Latex to write the manuscript for this project

Skills required:
1. Programming skills for Matlab
2. Modeling skills for ODE or PDE models
3. Know how to generate numerical solutions for ODE or PDE model by using Matlab
4. Willing to learn some biological data / background
5. Analysis skills for ODE model, including existence, uniqueness, and boundedness of solution, positive invariant set, local stability of equilibria, bifurcation analysis
6. Use Latex for manuscript editing

Research area: My research interests focus on control and optimization for dynamical systems, and their application to engineering and life science. I use methods at the intersection of differential equations, control and optimization theory, dynamical systems, and numerical analysis. This broad range of techniques finds application to stability and optimal control of dynamical systems; model predictive control; parameters’ estimation; the mathematical foundation of machine learning; stochastic optimal control and mathematical finance; the distribution of utilities over grids; optimal irrigation strategies and wastewater management; and the control of epidemics and pest management, as for the project described below.

Student roles:
The research project aims to provide a meaningful research experience to the student in an engrossing work environment. The student will engage in tasks typical to a research initiative in applied mathematics: studying the state-of-the-art literature and performing a comparative analysis among different contributions; familiarization with the research subject and its standard techniques; analyzing new problems by applying the acquired knowledge; developing theoretical computations or numerical simulations to derive desired conclusions from the system under consideration; and writing a report to describe the methodology of the analysis and the findings of the research activity. Assigned tasks may be oriented towards theoretical or numerical aspects of the problem, dependent on the background and preferences of the student. Work will be performed with the supervisor. The project does not include any lab experiments nor field work.

The student is expected to be eager to apply mathematical modelling techniques to describe wildfire dynamics and wildfire mitigation strategies, to have a proactive attitude in the daily research tasks and to communicate effectively with the team.

At the beginning of the internship, the student will benefit from two one-to-one meetings a week with the supervisor. After the first few weeks of the internship, the plan is to reduce the frequency of one-to-one meetings to one per week. During the meetings with the supervisor, both high-level and technical aspects of the problem will be addressed.

Additionally, the student will join the weekly meetings of the research group in control theory within the Department of Applied Mathematics of the University of Waterloo. The research group provides a diverse and inclusive environment counting 3 faculty members, 3 postdocs, 6 PhDs and 12 master's students. This will provide the student with an opportunity to engage with different topics in the same research area and interact with senior students.

Skills required:
The interested student should have a background in mathematics, physics or engineering, with a propensity for differential equations, mathematical modelling, and control theory.

The student is expected to be familiar with either theoretical or numerical aspects of partial and ordinary differential equations.
In terms of coding skills, suitable programming skills in either Matlab or Python language are beneficial.
Inclination to work in a team is key, as well as effective time management and good communication skills.

Previous exposure to problems in control theory, mathematical modelling, and application to environmental science would be a plus.

Research area: My research interests focus on control and optimization for dynamical systems, and their application to engineering and life science. I use methods at the intersection of differential equations, control and optimization theory, dynamical systems, and numerical analysis. This broad range of techniques finds application to stability and optimal control of dynamical systems; model predictive control; parameters’ estimation; the mathematical foundation of machine learning; stochastic optimal control and mathematical finance; the distribution of utilities over grids; optimal irrigation strategies and wastewater management; and the control of epidemics and pest management, as for the project described below.

Student roles:
The research project aims to provide a meaningful research experience to the student in an engrossing work environment. The student will engage in tasks typical to a research initiative in applied mathematics: studying the state-of-the-art literature and performing a comparative analysis among different contributions; familiarization with the research subject and its standard techniques; analyzing new problems by applying the acquired knowledge; developing theoretical computations or numerical simulations to derive desired conclusions from the system under consideration; and writing a report to describe the methodology of the analysis and the findings of the research activity. Assigned tasks may be oriented towards theoretical or numerical aspects of the problem, dependent on the background and preferences of the student. Work will be performed with the supervisor. The project does not include any lab experiments nor field work.

The student is expected to be eager to apply mathematical modelling techniques to describe pest management strategies, to have a proactive attitude in the daily research tasks and to communicate effectively with the team.

At the beginning of the internship, the student will benefit from two one-to-one meetings a week with the supervisor. After the first few weeks of the internship, the plan is to reduce the frequency of one-to-one meetings to one per week. During the meetings with the supervisor, both high-level and technical aspects of the problem will be addressed.

Additionally, the student will join the weekly meetings of the research group of the supervisor within the Department of Applied Mathematics at the University of Waterloo. The research group provides a diverse and inclusive environment counting 3 faculty members, 3 postdocs, 6 PhDs and 12 master's students. This will provide the student with an opportunity to engage with different topics in the same research area and interact with senior students.

Skills required:
The interested student should have a background in mathematics, physics or engineering, with a propensity for differential equations, mathematical modelling, and control theory.

The student is expected to be familiar with either theoretical or numerical aspects of ordinary differential equations.
In terms of coding skills, suitable programming skills in either Matlab or Python language are beneficial.
Inclination to work in a team is key, as well as effective time management and good communication skills.

Previous exposure to problems in control theory, mathematical modelling, knowledge of partial differential equations, or applications to environmental science would be a plus.

Research area: I am a mathematical biologist who specializes in infectious disease dynamics. My work is at the intersection of applied mathematics, theoretical biology, and ecology & evolution. I develop mathematical models in a variety of contexts, which include pathogen evolution, immuno-epidemiology, behavioural-epidemiology, and economic-epidemiology. The models I develop are generally systems of nonlinear differential equations, and which I then analyze analytically and/or numerically. Throughout, I use these models to seek and explain biological insight and intuition.

Student roles:
The student will analyze a mathematical model that couples human behaviour with epidemiological dynamics. This will be analytical, but likely at least partly numerical as well. They will be expected to generate figures that summarize their mathematical/computational results.

The student will also be expected to have regular meetings with the supervisor, and to attend all weekly group meetings. They will also be expected to interact with other members of the research group (especially those working on related projects).

Skills required:
Knowledge of nonlinear ordinary differential equations, linear algebra, and computer programming is essential. Familiarity with mathematical modelling and/or knowledge of biological concepts (e.g., infectious disease or ecology/evolution) are considered assets.

Research area: I am a mathematical biologist who specializes in infectious disease dynamics. My work is at the intersection of applied mathematics, theoretical biology, and ecology & evolution. I develop mathematical models in a variety of contexts, which include pathogen evolution, immuno-epidemiology, behavioural-epidemiology, and economic-epidemiology. The models I develop are generally systems of nonlinear differential equations, and which I then analyze analytically and/or numerically. Throughout, I use these models to seek and explain biological insight and intuition.

Student roles:
The student will analyze a mathematical model that couples immunological and epidemiological dynamics. This will be analytical, but likely at least partly numerical as well. They will be expected to generate figures that summarize their mathematical/computational results.

The student will also be expected to have regular meetings with the supervisor, and to attend all weekly group meetings. They will also be expected to interact with other members of the research group (especially those working on related projects).

Skills required:
Knowledge of nonlinear ordinary differential equations, linear algebra, and computer programming is essential. Familiarity with mathematical modelling and/or knowledge of biological concepts (e.g., infectious disease or ecology/evolution) are considered assets.

Research area: My research involves theoretical and numerical investigations of mathematical models for aggregation/swarming phenomena. While such phenomena arise in a variety of areas, we are particularly interested in applications of these models to machine learning (transformers), population biology (swarming or flocking of animals) and robotics. Various mathematical models exist in the literature, ranging from particle-based (ODE) to kinetic and continuum (PDE) descriptions. Most of these formulations lead to nonlinear and nonlocal differential equations which are challenging to analyze and simulate.

Student roles:
As noted above, the student will perform numerical and analytical investigations of an aggregation model on surfaces and manifolds. Depending on the strengths of the student, there are various directions that this project can evolve along. There would be excellent opportunities for a numerically-inclined student, as well as for a student interested in analysis. An incomplete list of various issues that can be studied in this project is: i) investigate numerically various interaction potentials, along with the equilibria that they yield; ii) set up the model on various manifolds (e.g, sphere and matrix manifolds, commonly used in machine learning and engineering applications); iii) look into the role of curvature in the asymptotic behaviour of the solutions; iv) investigate the long time behaviour of solutions in terms of the diffusion strength.

Skills required:
The student should have a solid mathematical training, in particular in analysis and differential geometry. The student should also be familiar with basic numerical analysis (e.g., basic numerical linear algebra and numerical integration of ODEs). Some experience with coding in Matlab is strongly desired.

Research area: I am a mathematical biologist who specializes in infectious disease dynamics. My work is at the intersection of applied mathematics, theoretical biology, and ecology & evolution. I develop mathematical models in a variety of contexts, which include pathogen evolution, immuno-epidemiology, behavioural-epidemiology, and economic-epidemiology. The models I develop are generally systems of nonlinear differential equations, and which I then analyze analytically and/or numerically. Throughout, I use these models to seek and explain biological insight and intuition.

Student roles:
The student will analyze a mathematical model. This will be analytical, but likely at least partly numerical as well. They will be expected to generate figures that summarize their mathematical/computational results.

The student will also be expected to have regular meetings with the supervisor, and to attend all weekly group meetings. They will also be expected to interact with other members of the research group (especially those working on related projects).

Skills required:
Knowledge of nonlinear ordinary differential equations, linear algebra, and computer programming is essential. Familiarity with mathematical modelling and/or knowledge of biological concepts (e.g., infectious disease or ecology/evolution) are considered assets.

Research area: I am broadly interested in delay differential equations, including state-dependent delay differential equations and numerical methods for approximating solutions of DDEs. I am also interested in many fields of mathematical modeling, and particularly in transient dynamics such as the honeymoon period of disease systems after the start of mass vaccination campaigns.

Student roles:
We will begin by preparing a modern review of transient dynamics, including both theory and applications. The focus will be in systems of ordinary differential equations, but we will also make connections to delay equations and stochastic systems. Depending on the interest of the student, we can also work on further developing the theory of transient centers (Liu and Magpantay 2022) or developing software packages for detecting interesting transient dynamics.

Skills required:
Background in applied dynamical systems (ODEs, numerical methods)

Research area: I work on mathematical aspects of atomistic simulation, coarse-graining, multi-scale modelling and machine learning. My research is highly interdisciplinary, ranging from rigorous mathematical analysis to model development. At the theoretical end I develop and analyze mathematically formalised models and numerical algorithms. At the applied end, I collaborate closely with modellers to use new mathematical ideas in the development of practical models for materials and molecules. A current focus is the usage of machine-learning and data-science tools in the context of coarse-graining and multi-scale modelling, across all scales from elementary particles to continuum mechanics.

Student roles:
(1) Initial background reading and introduction to the subject.
(2) Student and advisor will narrow the project down to a specific task involving a new method that fills a gap in our current methodology. At the same time the student and advisor will formulate a range of benchmark problems ranging from academic examples to realistic modelling scenarios.
(3) Testing of existing methodology on the benchmark problems to gain experience and provide a baseline.
(4) Development, implementation, numerical testing of new error prediction algorithms.
(5) Optionally develop rigorous mathematical analysis of new algorithms for a mathematically more ambitious project.
(6) Document project, first as a report with the aim of incorporating it into a publication within the wider research programme; and secondly, document any new codes that have been written.

Supervision arrangements:
- The student will normally meet weekly with the advisor, join weekly group meetings, and normally also be paired with a graduate student or postdoc for additional support.
- The student will be embedded in an applied mathematics research group at UBC, and in addition have the opportunity to collaborate with modelling research groups around the world, e.g., in Cambridge, Warwick, Bochum.
- The student will be provided with access to required computing infrastructure.

Skills required:
BACKGROUND: The student will have a strong background in one of
- computational mathematics, numerical analysis, scientific computing, inverse problems
- machine-learning
- computational statistics, baysian statistics, uncertainty quantification

MOTIVATION: The student should be motivated
- to contribute to interdisciplinary research project and be open to engage in cross-disciplinary collaborations.
- and have the confidence to drive the direction of the research (with help and close guidance by the advisor)

CODE DEVELOPMENT:
- Some programming experience is essential. The advisor and research group will help the student in contributing to our existing code base if and as needed.

Research area: This project would be jointly supervised by Dr. Adam Van Tuyl (McMaster) and Dr. Kevin Vander Meulen (Redeemer and adjunct at McMaster). Dr. Van Tuyl's main area of interest is commutative algeba and its applications to combinatorics. Dr. Vander Meulen is interested in combinatorial matrix theory, that is, using results from combinatorics, like graph theory, to prove results about matrices. They have worked together on a number of projects with undergraduates, including past Mitacs projects, and have co-authored research articles with students.

Student roles:
For this project, it is expected that the student would help the project in the following ways:

1) Search the literature for relevant research articles. This search would include using online academic databases (e.g. MathSciNet), and using the McMaster science library.

2) Understand the definition of a matrix pattern and related concepts (this will be explained to the student during the first few weeks of the program).

3) Once the definitions are understood, formulate new examples and conjectures using specialized computer programs (like Sage).

4) The student would be expected to write up their results using LaTeX (this will be taught to the student).

5) When possible, the student will help prove some of their conjectures.

The student will interact with the professor and likely another undergraduate student, as a team approach to the research problem. The student will also participate in writing up any results discovered over the research term.

Skills required:
The ideal student will have the following skills/background:

* A course in linear algebra (in particular, he or she will have covered eignenvalues and eigenvectors)
* Some programming experience (any language)

In addition, a course in discrete mathematics or graph theory would be an asset, but it is not required. We would provide the necessary background.

Research area: My research program is dedicated to translating insights derived from non-invasive neuroimaging modalities, specifically electroencephalography (EEG), magnetoencephalography (MEG), and magnetic resonance imaging (MRI), into clinically relevant applications for brain disorders. Leveraging my dual affiliation as a scientist at Simon Fraser University and within local public hospitals, I explore how variability and pathological alterations in these brain signals manifest across diverse neurological populations and throughout typical development and ageing processes. A central aim is to elucidate the functional correlates of this neurophysiological variability, with the ultimate goal of developing and validating clinically translatable computational methods that enhance diagnostic accuracy.

Student roles:
The student intern's primary responsibility will be to analyze associations between medications and electroencephalograms (EEGs) from an extensive clinical database. This will involve employing advanced statistical techniques (largely in Python), including predictive analytics and machine learning models, to identify correlations and potential predictive relationships. Key tasks include data preprocessing, feature extraction, model development, and validation of analytical pipelines.
A significant component of this role involves disseminating research outcomes. The intern will be expected to contribute substantially to, and potentially lead, the preparation of a research manuscript suitable for peer-reviewed publication. This will entail articulating the study's rationale, methodology, results, and their broader scientific implications.
Furthermore, the intern will actively collaborate with other students and researchers within the broader research initiative focused on clinical EEG and data science applications. This collaborative engagement is crucial for exchanging knowledge, addressing methodological challenges, and advancing the collective development of AI tools in clinical neurophysiology and healthcare.

Skills required:
The ideal candidate for this internship will possess a strong academic background in a quantitative discipline. This typically includes fields such as Mathematics, Statistics, Computer Science, Physics, Engineering, or a closely related area with a significant analytical component, providing the foundational knowledge necessary for complex data analysis and modeling.
Familiarity with Python is beneficial, as it will be the primary tool for data manipulation, analysis, and algorithm implementation within this project.
Furthermore, the candidate should have an understanding of statistical principles and techniques. Prior experience applying machine learning concepts, even in academic coursework or personal projects, would be advantageous.

Research area: My research is broadly on the development of theoretical and computational models to describe the interaction of light with atoms, molecules and nanostructures. It is at the intersection of quantum control, quantum optics, quantum computing, quantum sensing, and ultrafast science. We work on multiple platforms such as trapped-ions, Rydberg atoms, quantum dots, atoms in cavities, etc. Applications include designing quantum sensors for sensitive bio/chemo marker detection, developing protocols for advancing quantum information, and modelling high-harmonic generation from solids.

Student roles:
The student will study the literature on microwave quantum computing using trapped ions, specifically Ytterbium. They will meet with me at least weekly to discuss their progress and present their plans. They will create an end of internship report, and present a poster at the Quantum Day symposium.

Skills required:
Third/Fourth year course in quantum mechanics, including quantized harmonic oscillator creation and annihilation operator formalism.
Good communication skills

Research area: This project is in the area of operations research, health economics, and mathematical modeling. It focuses on how pricing and reimbursement policies influence competition among pharmaceutical companies and affect healthcare costs. The project combines analytical modeling, optimization, simulation, and data analysis to study decision-making in healthcare systems. Students will gain exposure to mathematical modeling techniques and learn how quantitative methods can be used to evaluate policy and business decisions in regulated markets.

Student roles:
The student will participate in a research project investigating pricing and competition in pharmaceutical markets. Responsibilities may include reviewing academic literature, summarizing research findings, developing mathematical models, conducting computational experiments, analyzing results, and assisting with the preparation of reports and research documents.

The student will work closely with the supervisor through regular meetings and will receive guidance on research methods, model development, and scientific communication. Depending on their interests and background, the student may contribute to simulation studies, optimization models, data analysis, or policy-oriented evaluations.

The project offers an opportunity to gain experience in quantitative research while learning how mathematical and analytical tools can be applied to real-world healthcare and policy challenges. Students will develop skills in problem solving, critical thinking, research communication, and computational analysis that are valuable for both graduate studies and industry careers.

Skills required:
Students from mathematics, statistics, analytics, economics, and industrial engineering, or related fields, are encouraged to apply. Familiarity with calculus, basic probability, and mathematical reasoning is needed. Some programming experience (Python or Mathematica) is desirable but not required. Strong analytical thinking, curiosity, and willingness to learn new quantitative methods are more important than prior knowledge of pharmaceutical markets.

Research area: My specialized research area is applied mathematics and mathematical biology, with a focus on dynamical systems, reaction–diffusion equations, pattern formation, and stochastic modeling. I study how complex spatial and temporal patterns arise in biological and physical systems, using tools from differential equations, asymptotic analysis, perturbation methods, stability theory, and numerical simulation. In particular, my research includes the analysis of nonlinear partial differential equation(PDE) and ordinary differential equation(ODE) models, epidemic and ecological dynamics, localized patterns such as spikes and mesas, and the effects of noise, domain growth, and adaptive feedback on pattern formation and stability.

Student roles:
The student will play an active role in developing and analyzing mathematical models for wildfire–vegetation–moisture interactions. They will begin by learning the background of reaction–diffusion systems, ecological pattern formation, wildfire dynamics, and Turing instability. This will provide the foundation for building a simplified model that describes the feedback between fire activity, vegetation or fuel density, and soil moisture or water availability.

I will mentor the student in carrying out mathematical analysis, including the study of spatially homogeneous steady states, linear stability, and diffusion-driven instability. In particular, the student will help derive and analyze the conditions under which a uniform steady state becomes unstable and spatial patterns may emerge. Numerical simulations will be used to support and guide the analysis. The student will implement the model in MATLAB, Python, or a similar platform, generate one- and two-dimensional simulations, explore parameter regimes, and compare homogeneous, patterned, and transient wildfire-related dynamics. They will also prepare figures to illustrate the analytical and computational findings.

Throughout the project, I will meet regularly with the student to discuss mathematical ideas, interpret simulation results, and refine the model. I will also mentor them in key academic competencies, including mathematical modeling, stability analysis, numerical experimentation, scientific visualization, and research communication. By the end of the internship, I will guide the student in summarizing the main findings in a short report or, depending on progress, a manuscript for publication.

Skills required:
The student should have a background in mathematics, applied mathematics, physics, engineering, computer science, or a related quantitative field. Basic knowledge of ODEs, PDEs, numerical methods, and mathematical modeling would be helpful. Since the project involves simulations of reaction–diffusion systems, some programming experience in MATLAB, Python, or a similar language is strongly preferred. Prior knowledge of dynamical systems, ecological modeling, pattern formation, or Turing instability would be an asset, but is not required. The student should be curious, motivated to learn new mathematical and computational tools, and interested in applying mathematics to environmental and wildfire-related problems.

Research area: Our research lies in mathematical epidemiology, focusing on multiscale modeling of infectious and chronic diseases. We develop dynamical systems that integrate within-host immune dynamics, population-level transmission, and social determinants of health, with applications to vector- borne diseases, syndemics, and comorbidity dynamics. Our work incorporates climate-driven processes, host-pathogen interactions, and health inequities. Methodologically, we use applied differential equations, singular perturbation theory, and data-driven approaches such as Bayesian inference. We also integrate artificial intelligence and machine learning, including neural differential equations, to enhance model calibration, flexibility, and predictive capability.

Student roles:
The student will play a central role in implementing, analyzing, and calibrating a climate-driven
mosquito-bird-human transmission model. The internship will begin with data collection and
preprocessing, where the student will compile temperature time-series data from Environment
and Climate Change Canada and obtain epidemiological and mosquito surveillance data from
relevant public health sources. The student will ensure consistency in temporal resolution and
prepare datasets for model integration.
The student will then implement the mathematical model computationally using R or MATLAB,
incorporating temperature-dependent parameters governing mosquito development, survival, and
transmission. A major component of the role involves parameter estimation using Bayesian
inference techniques, including implementation of Markov Chain Monte Carlo (MCMC)
methods to fit the model to observed data.
The student will conduct sensitivity and uncertainty analyses to identify key drivers of disease
dynamics and assess robustness of model predictions. They will also perform scenario analyses
to evaluate the impact of temperature variability and climate change on transmission patterns.
In addition, the student will contribute to model validation by comparing simulated outputs with
empirical data. Documentation of methods, code development, and interpretation of results will
be required throughout the project.
The student will actively participate in research discussions, contribute to report writing and
presentations for dissemination.

Skills required:
The student should have a strong background in mathematics, applied mathematics, statistics, or
a related field. Familiarity with differential equations, basic epidemiological modeling, and data
analysis is required. Experience with programming in R, MATLAB, or Python is essential.
Knowledge of statistical inference methods, particularly Bayesian approaches, is highly
desirable. Prior exposure to infectious disease modeling, dynamical systems, or ecological
modeling will be an asset. The student should also demonstrate strong analytical thinking,
problem-solving ability, and scientific communication skills.

Research area: Computer communications and networks, particularly protocol design, performance analysis and applied network security.

Student roles:
The intern student will work with faculty members and graduate students, learning through the research process and helping with simulation, as well as experimenting on a testbed. For more information about the research program and the related projects, please refer to http://web.uvic.ca/~pan and the references therein.

Skills required:
Interested in cloud computing and data-center networking, and having a basic knowledge on computer networks and operating systems, with a good skill in computer programming (C/C++, Java or Python). Any experience with network simulators or testbeds is a plus.

Research area: Number theory is the study of the questions related to integral numbers: 1 ,2, 3, ... A central question in Number Theory is the resolution of equations involving integral (or rational) numbers. Two of the most famous open problems in this area are the Riemann hypothesis and the Birch--Swinnerton-Dyer conjecture (BSD), both are included in the Seven Millennial Problems proposed by the Clay Institute. Both problems deal with properties of L-functions and the deep connections to arithmetics. My research program lies in the study of generalizations of these conjectures.

Student roles:
The student will start by learning the theory of finite fields, then basic results about polynomials defined over finite fields, then progress to the Riemann zeta function and the prime number theorem for polynomials. We will then pass to discuss Dirichlet L -series and primes in arithmetic progressions and other topics as time permits. The initial background will be covered by following the first 4-5 chapters of the book "Number Theory in Function Fields" by Rosen. We will then progress towards reading research articles in the area, such as "Moebius functions of order k in function fields" by Hwanyup Jung and "A variant of Collatz’s Conjecture over Binary Polynomials" by Luis H. Gallardo and Olivier Rahavandrainy

In order to do this, the student will meet the professor regularly (about once a week) to discuss the study topics and problems. The student may also be required to occasionally attend seminars and to interact with local students.

Skills required:
It is highly recommended that the student know about finite fields and general field theory.

Research area: Numerical analysis of partial differential equations (PDEs), optimization, numerical linear algebra, PDEs

Student roles:
- learn about finite difference or spectral methods for solving differential equations
- read some papers on the numerical solution of the Willmore differential equation
- implement a finite difference method to solve the problem using MATLAB
- determine the bifurcation diagram
- time permitting, implement a spectral method to solve the problem

Skills required:
The applicant should have taken courses in linear algebra, multi-variable calculus and differential equations. Those having previous exposure to numerical analysis and computer programming are strongly preferred.

Research area: This research focuses on the dynamical behavior of hybrid quantum systems, particularly interactions between electromagnetic fields and atomic systems. It spans quantum information, quantum correlations, and quantum batteries, with an emphasis on applying quantum measurements to enhance communication and energy storage applications. We have developed new protocols for quantum battery charging and investigated the role of entanglement in rapid energy transfer between qubits. More broadly, this research applies the principles of quantum mechanics to optimize quantum battery performance, including studies on environmental effects and high-dimensional quantum systems.

Student roles:
The student will work as a computational researcher under the supervision of a PhD student and the faculty supervisor on projects related to quantum battery modeling and analysis. The position will provide hands-on experience in computational physics, quantum systems, data analysis, and scientific research practices. The student will contribute to the implementation and evaluation of quantum battery models using numerical simulations and data-driven analysis techniques.

Skills required:
Since this project involves numerical simulation algorithms for quantum battery models, I believe that students with mathematical and physical backgrounds are welcome. Furthermore, computer science and engineering backgrounds are accepted. Knowledge of Python libraries such as Numpy, Qutip, Matplotlib, Scikit-learn, and Pandas is required. Linear algebra, differential equations, probability, and machine learning courses are beneficial.

Research area: I use discrete mathematics and deterministic operations research tools to solve scheduling problems. I also work in the area of Ramsey Theory. Specifically, I work on obtaining proofs for the values of Ramsey Numbers.

Student roles:
The student will begin by reading the existing literature in the area of Ramsey numbers, including the available proofs of the known values of Ramsey numbers. Working under the guidance of the professor and using ideas developed by the professor, the student will begin by developing new proofs of known values of Ramsey numbers of the form R(3,n). These techniques will subsequently be used to obtain values for R(3,10) and other Ramsey numbers for which values are currently unknown.

Skills required:
The student should be currently studying mathematics or computer science. (A background in engineering or in any other field would not be appropriate.) The student should have taken one or more courses in graph theory. Programming skills and experience would be useful but are not essential.

Research area: My research interests are primarily in Operations Research, with a focus on optimization methods for sustainable transportation systems and public infrastructure. I work on public transit optimization, electric vehicle charging infrastructure planning, and models that incorporate realistic user behavior. My research develops innovative Operations Research techniques for complex, real-world transportation problems. Methodologically, I combine traditional optimization tools, such as mathematical programming and combinatorial optimization, with machine learning and simulation-based optimization approaches.

Student roles:
The student will contribute to the design and implementation of an open-source simulator for passenger flows in metro networks. The student will help develop the demand reconstruction module, implement the passenger-flow simulation engine, and define realistic test scenarios based on metro network structure, timetable data, station-level demand, and train capacity constraints. The student will also conduct computational experiments to evaluate how accurately the simulator reproduces passenger movements, identifies crowding patterns, and supports the analysis of waiting times, denied boarding, transfer congestion, and capacity bottlenecks.

The internship will take place at Concordia University, and the Interuniversity centre of network logistics (CIRRELT), both in Montreal. The student will be able to participate in activities (seminars etc.) at all of these places.

Skills required:
Required skills/background of the student: The ideal candidate will have a strong background in operations research, industrial engineering, applied mathematics, or a related discipline. Familiarity with mathematical optimization (LP, MILP) is required. Knowledge of reliability engineering, stochastic processes, and degradation modeling is considered an asset. Experience with programming languages such as Python, MATLAB, or C++, as well as optimization solvers such as Gurobi or CPLEX, is advantageous.
Exposure to heuristic or metaheuristic optimization methods is also beneficial. Most importantly, we seek a motivated and curious student with strong analytical skills and a willingness to learn.

Research area: - Numerical partial differential equations (wavelet and finite difference methods for interface and wave propagation problems) - Scientific machine learning (operator learning, hybrid models) - Numerical linear algebra (hierarchical structured matrices) - Applications of wavelet methods in data science

Student roles:
Perform literature review, build operator learning models, and conduct extensive numerical experiments.

Skills required:
- Strong scientific computing, numerical analysis, and programming skills.
- Basic knowledge of partial differential equations.
- Good mathematical skills (reasonably comfortable with proofs).

Research area: My specialized research area is mathematical biology, with a focus on partial differential equation models for structured populations. I study how biological populations evolve, persist, spread, or decline in heterogeneous and changing environments. My work uses tools from PDEs, long-time asymptotic analysis, optimal control, and dynamical systems to understand questions related to population persistence, spatial organization, resource distribution, and epidemic dynamics. I am particularly interested in models where ecological or epidemiological processes interact with spatial structure, environmental variation, or management strategies.

Student roles:
The student will contribute to the numerical exploration of structured population models in heterogeneous environments. Their main role will be to implement and run simulations comparing different spatial arrangements of resources and studying their effects on population persistence or extinction. The student will review a small set of background materials, help formulate simple model scenarios, write or adapt numerical code, generate plots, and analyze the resulting population dynamics.

By the end of the internship, the student is expected to produce clear numerical comparisons, summarize the main observations, and prepare a short written report describing the models, methods, simulations, and conclusions. They are expected to present their work at the Math-Bio seminar. The project will be supervised regularly, but the student should be able to work independently between meetings and document their code and results clearly.

Skills required:
The student should have a strong background in undergraduate mathematics, including differential equations, linear algebra, and basic numerical methods. Some familiarity with partial differential equations, reaction-diffusion models, or mathematical biology would be useful, but is not required. The project will be computational, so the student should be comfortable programming in Python, MATLAB, Julia, or a similar language, and should be able to produce clear plots and numerical comparisons.

The ideal student is interested in applying mathematics to ecological or biological questions, can work independently, and is willing to learn basic numerical techniques for simulating population models in heterogeneous environments.

Research area: Partial differential equations; Applied analysis.

Student roles:
Perform calculations at the multivariable calculus level; Conduct numerical experiments.

Skills required:
Solid foundation in multivariable calculus; Basic programming skills.

Research area: My research interests are primarily in Operations Research, with a focus on optimization methods for sustainable transportation systems and public infrastructure. I work on public transit optimization, electric vehicle charging infrastructure planning, and models that incorporate realistic user behavior. My research develops innovative Operations Research techniques for complex, real-world transportation problems. Methodologically, I combine traditional optimization tools, such as mathematical programming and combinatorial optimization, with machine learning and simulation-based optimization approaches.

Student roles:
The student will contribute to the formulation of the special-event timetabling problem, the implementation of the optimization model, and the development of an algorithmic solution approach. The student will also help define realistic event-demand scenarios, identify relevant operational constraints such as train capacity and feasible short-turning locations, and conduct computational experiments to evaluate the resulting timetables. The evaluation will focus on how specialized event timetables improve passenger waiting times, platform crowding, and capacity utilization during periods of extreme but predictable demand.

The internship will take place at Concordia University, and the Interuniversity centre of network logistics (CIRRELT), both in Montreal. The student will be able to participate in activities (seminars etc.) at all of these places.

Skills required:
Required skills/background of the student: The ideal candidate will have a strong background in operations research, industrial engineering, applied mathematics, or a related discipline. Familiarity with mathematical optimization (LP, MILP) is required. Knowledge of reliability engineering, stochastic processes, and degradation modeling is considered an asset. Experience with programming languages such as Python, MATLAB, or C++, as well as optimization solvers such as Gurobi or CPLEX, is advantageous.
Exposure to heuristic or metaheuristic optimization methods is also beneficial. Most importantly, we seek a motivated and curious student with strong analytical skills and a willingness to learn.

Research area: My research interests are primarily in Operations Research, with a focus on optimization methods for sustainable transportation systems and public infrastructure. I work on public transit optimization, electric vehicle charging infrastructure planning, and models that incorporate realistic user behavior. My research develops innovative Operations Research techniques for complex, real-world transportation problems. Methodologically, I combine traditional optimization tools, such as mathematical programming and combinatorial optimization, with machine learning and simulation-based optimization approaches.

Student roles:
The student will contribute to the formulation of the transition-period metro timetabling problem, the implementation of the optimization model, and the development of an algorithmic solution approach. The student will also help define realistic transition scenarios between periodic service regimes, identify relevant operational constraints such as train capacity, rolling-stock availability, turnaround operations, and infrastructure limitations, and conduct computational experiments to evaluate the resulting timetables. The evaluation will focus on how optimized transitional timetables improve service regularity, passenger waiting times, rolling-stock utilization, and operating costs when metro lines switch between different periodic service patterns.

The internship will take place at Concordia University, and the Interuniversity centre of network logistics (CIRRELT), both in Montreal. The student will be able to participate in activities (seminars etc.) at all of these places.

Skills required:
Required skills/background of the student: The ideal candidate will have a strong background in operations research, industrial engineering, applied mathematics, or a related discipline. Familiarity with mathematical optimization (LP, MILP) is required. Knowledge of reliability engineering, stochastic processes, and degradation modeling is considered an asset. Experience with programming languages such as Python, MATLAB, or C++, as well as optimization solvers such as Gurobi or CPLEX, is advantageous.
Exposure to heuristic or metaheuristic optimization methods is also beneficial. Most importantly, we seek a motivated and curious student with strong analytical skills and a willingness to learn.

Research area: My specialized research area is community-oriented artificial intelligence, mathematical modeling, and data science for infectious disease prevention, preparedness, and response. I develop AI-enabled and mathematical modeling approaches to support public-health decision-making, with emphasis on epidemic dynamics, behavioral responses, vaccination strategies, climate and environmental drivers, and health equity. This research integrates epidemiological data, climate-informed modelling, and community-relevant analytics to address infectious disease challenges in Canada, Africa, and the Global South, while supporting resilient health systems and equitable outbreak response.

Student roles:
The student will develop and implement Physics-Informed Neural Network models that embed epidemiological equations into neural-network training. They will collect and process epidemic, mobility, vaccination, demographic, behavioural, and information-diffusion data; train and validate models; recover time-varying epidemiological parameters; and compare results with AI baselines such as LSTMs, transformers, and neural ODEs. The student will prepare simulations, visualizations, and forecasting outputs, and contribute to presentations and manuscript writing in collaboration with supervisors and interdisciplinary partners

Skills required:
The ideal student should have a background in artificial intelligence, data science, applied mathematics, computer science, machine learning, statistics, mathematical epidemiology, public health, or a related field. Familiarity with neural networks, differential equations, SEIR-type models, forecasting, optimization, and health data analysis is preferred. Experience with Python, PyTorch, TensorFlow, R, or scientific computing tools would be an asset. Strong coding, mathematical reasoning, analytical, writing, and communication skills are required.

Research area: My research focuses on systems and control theory, with particular emphasis on time-delay systems, hybrid systems, event-triggered control, impulsive control, networked dynamical systems, and stability analysis. My work combines mathematical analysis and control design to develop rigorous theoretical tools for studying complex dynamical systems arising in engineering, biological, and cyber-physical applications. Recent research interests include positivity-preserving dynamics, Halanay-type inequalities, event-triggered stabilization, synchronization of complex networks, and dynamical systems on time scales.

Student roles:
The student will:

• Conduct a literature review on positivity theory, functional differential equations, and dynamical systems with delays.

• Study classical positivity results and comparison principles for delayed dynamical systems.

• Assist in developing new positivity-preserving conditions and comparison theorems for systems on time scales and networked systems.

• Perform mathematical analysis under the supervision of the research team.

• Develop numerical examples and simulation studies to validate theoretical findings.

• Participate in weekly research meetings and present progress reports.

• Contribute to the preparation of technical reports, conference presentations, and potentially journal publications.

Skills required:
• Strong background in mathematics, applied mathematics, or related disciplines.

• Familiarity with differential equations and linear algebra.

• Knowledge of real analysis, stability theory, or functional differential equations is desirable but not mandatory.

• Experience with MATLAB, Python, or similar computational software for numerical simulations.

• Strong analytical and problem-solving skills.

• Interest in mathematical modelling and theoretical research.

Research area: My research focuses on operations research, optimization, machine learning, and healthcare analytics. I develop predictive models and analytical methods to support decision-making in healthcare systems and pharmaceutical supply chains. My work combines optimization, statistical modeling, regression analysis, classification techniques, and machine learning to address real-world challenges in healthcare management. Through these approaches, I aim to improve resource allocation, enhance patient outcomes, and support more efficient and effective healthcare operations.

Student roles:
The student will participate in all major stages of this research project, which focuses on predicting patient Length of Stay using machine learning techniques.

**Literature Review:**
The student will review recent academic research on Length of Stay prediction and healthcare analytics. They will summarize key findings, identify common approaches, and explore opportunities for improving prediction accuracy.

**Data Preparation:**
The student will assist in cleaning, organizing, and preparing healthcare data for analysis. Tasks may include handling missing values, exploring variables, transforming data, and preparing datasets for machine learning applications.

**Model Development:**
The student will help implement and evaluate machine learning models, including both regression models (predicting LOS as a numerical value) and classification models (predicting short versus long stays).

**Model Evaluation and Analysis:**
The student will compare model performance using appropriate evaluation measures and investigate which patient characteristics contribute most to prediction accuracy.

**Research Communication:**
The student will assist with preparing figures, summaries, reports, and presentations describing the methods, findings, and practical implications of the research.

This project provides hands-on experience in machine learning, healthcare analytics, predictive modeling, and data-driven decision-making while contributing to research with meaningful applications in healthcare management.

Skills required:
The student should have a background in data science, machine learning, statistics, computer science, operations research, engineering, or a related field. Familiarity with programming languages such as Python or R is desirable. Experience with predictive modeling, data analysis, or machine learning techniques would be beneficial but is not required. An interest in healthcare applications is an asset. Strong analytical thinking, problem-solving ability, and communication skills are important for interpreting results and contributing effectively to the project.

Research area: 1. Data Analysis. 2. Privacy-Preserving Analysis. 3. Graph Mining. 4. Parallel and Distributed Computing.

Student roles:
Students will first conduct a literature review of existing work on differential privacy and graph analysis to understand current methods, limitations, and research gaps. They will then be responsible for developing algorithms to identify specific subgraph patterns while ensuring privacy preservation. This involves analyzing and optimizing error bounds to guarantee the effectiveness of the algorithms under differential privacy constraints. Students will also implement the algorithms, evaluate their performance on real-world datasets, and contribute to writing comprehensive reports detailing the findings, methodologies, and outcomes of the project.

Skills required:
The ideal candidate should be a junior or senior undergraduate majoring in Mathematics or Computer Science, or a related field, with a good understanding of probability theory, algorithms, and data structures. Basic coding skills in Python/Go or a similar language are required to implement and test algorithms. The candidate should be able to analyze complex problems and communicate findings clearly in both written and verbal formats.

Research area: I am broadly interested in algebriac number theory and the theory of elliptic cures. Questions I study lie at the intersection of Iwasawa theory and arithmetic statistics. Iwasawa theory is a branch of algebraic number theory that studies the growth of arithmetic objects, like ideal class groups or Selmer groups of elliptic curves, in infinite towers of number fields. A long-term goal is to understand the average behaviour of the Iwasawa invariants in appropriate families. I am also interested in questions pertaining to Iwasawa theory of graphs. I also think about questions related to Diophantine stability and Hilbert’s 10th Problem.

Student roles:
The student will spend some time learning the background material before pursuing independent and original research in this area; this will include reading textbooks and research-level published articles. Aside from discussing with me, they will have an opportunity to interact and discuss mathematics with my graduate students.

Based on their readings and calculations, they will try to formulate conjectures in this direction and also prove some of the conjectures they formulate. Along the way, I will provide regular guidance. To develop intuition and formulate reasonable conjectures, they will be encouraged to perform computer experiments.

They will write a written report of their findings, and if they make enough progress I will provide guidance and support to try and publish the results.

Skills required:
1. It would benefit the student if they have some background in algebra and algebraic (and analytic) number theory. Knowledge of p-adic numbers would be helpful.
2. If the student is somewhat comfortable using Python, C, C++, or SAGE/ PARI/GAP that would be advantageous
3. Most important is to come with an open mind.

Research area: My research sits at the interface of geometry, soft matter, and materials science. My core focus is the design, fabrication, and modeling of soft materials, primarily hydrogels and elastomers, that undergo programmed shape transformations in response to environmental stimuli such as humidity or temperature. Drawing on principles from differential geometry and continuum mechanics, I develop mathematical frameworks to design differential growth fields that are encoded into responsive materials during fabrication, directing their transformation into target three-dimensional shapes. Potential applications range from soft robotics and 4D printing to biomimetic structures and biomedical devices.

Student roles:
The student will lead the research project, contributing across both its theoretical and computational dimensions. They will begin by conducting a thorough review of the relevant literature, building familiarity with the geometric formulation of elasticity, shape-morphing materials, and the mechanics of growing elastic sheets. This foundation will prepare them to engage meaningfully with the project's open research questions.
The core of the student's work will be semi-analytical, involving two complementary activities. On the analytical side, they will extend our theoretical framework to predict mechanical properties arising from geometric frustration and use it to derive design heuristics for promising material candidates. On the computational side, they will implement and run numerical simulations based on our existing numerical pipeline, including finite-element models and optimization routines, to test their theoretical predictions and explore parameter spaces that are not tractable analytically.
Beyond their individual research tasks, the student will be a full participant in the intellectual life of the group. They will attend regular one-on-one meetings with the PI and weekly group meetings where ongoing projects are discussed and ideas are exchanged. The student will be expected to present their progress and findings to the group on a regular basis, developing their ability to communicate technical work clearly and incorporate constructive feedback. By the end of the internship, they will deliver a final presentation summarizing their contributions and situating them within the broader project.
Overall, the student will be treated as a junior research collaborator: someone who both learns from the group's expertise and contributes original effort toward advancing the project's goals. The experience is designed to develop their research skills, deepen their scientific knowledge, and give them a genuine sense of ownership over their work.

Skills required:
The ideal candidate has a background in physics or applied mathematics.

Required: Strong proficiency in numerical computation (preferably Python or MATLAB); a solid foundation in classical mechanics, multidimensional calculus, and ordinary and partial differential equations; and the ability to independently review, analyze, and synthesize scientific literature.

Assets: Familiarity with differential geometry, continuum mechanics, finite-element modeling (FEM), or high-dimensional optimization.

An ability to bridge theory and computation, and an interest in connecting mathematical structure to physical behavior, are highly valued.

Research area: I am primarily interested in problems that lie at the intersection of representation theory with other areas, such as combinatorics, mathematical physics, number theory, and theoretical foundations of quantum computing. Roughly speaking, the goal of representation theory is to study realizations of complex algebraic structures using tools from linear algebra. One of the focal points of my research has been the study of Lie superalgebras, which are purely algebraic objects that first occurred in a highly influential but so far unproven theory in particle physics known as "supersymmetry".

Student roles:
The minimum requirement for the student is to prepare a summary of the research outcomes of the project as a 10-15 page expository report (typeset using LaTeX). Significant results established by the students throughout the project can lead to a research paper in a peer-reviewed publication venue. The student will meet with the supervisor once a week to report on the progress and discuss the challenges that arise along the way. The student should also prepare a short talk (20-30 minutes) for an departmental undergraduate conference. The project begins with acquiring the necessary background on the theory of quantum computation and representation theory of groups. Subsequently the student switches to leaning about a variety of problems that lie at the intersection of these two domains. The relevant references (mostly lectures and research papers) will be provided by the supervisor at various stages of the project.

Skills required:
Strong background in linear algebra and basic theory of groups, rings and fields is required.
Familiarity with some introductory concepts in combinatorics, e.g., integer partitions, Ferrer
diagrams, and graph theory, will be useful but not mandatory. Applicants are highly encouraged to improve their typesetting skills (particularly with LaTeX) prior to starting the project.Typesetting skills are vital for the progress of the project and dissemination of the outcomes.

Research area: My research focuses on modelling and optimizing performance of cloud-based systems. In particular, I am interested in optimizing resource allocation (i.e. the distribution of mobile application tasks to resources such as smartphones and servers) to reduce application execution times, battery usage of the energy-constrained resources, and communication time among resources. Recently, my group has been investigating potential quantum advantages in addressing the resource allocation problem. To date, we have developed a quantum‑based approach that applies the Quantum Approximate Optimization Algorithm (QAOA) to identify task allocations that minimize application execution time.

Student roles:
Recently, my research group has formulated a closed-form equation in the form of a Quadratic Unconstrained Binary Optimization (QUBO) problem to predict execution time of a mobile application [1]. This work also involved solving the QUBO using the Quantum Approximate Optimization Algorithm (QAOA). The student’s role in this project will be to solve the existing QUBO using a different computing method known as Quantum Annealing. The student will begin with developing an understanding of resource allocation in mobile cloud computing, followed by an investigation into the principles and mechanics of Quantum Annealing. It is important to note that QAOA and Quantum Annealing operate in fundamentally different ways. QAOA requires transforming a QUBO into a cost Hamiltonian, mapping that Hamiltonian to a digital quantum circuit, and then running the circuit iteratively while adjusting the angle parameters of the circuit until a classical optimizer converges on an optimal set of the parameters. In contrast, Quantum Annealing maps the QUBO directly onto the physical qubit architecture of an analog quantum device called an annealer. The annealer then performs a physical annealing cycle without any iterative parameter‑tuning loop. In practice, the annealer’s default parameters are effective for a wide range of real‑world optimization problems.

In this project, the student will learn to use a quantum annealer developed by D‑Wave Systems and will aim to solve our existing QUBO on this hardware. The expected outcome for the student is to successfully implement Quantum Annealing for a given resource allocation problem, assess the quality of the resulting solution (i.e. near-optimal allocation), as well as measuring and evaluating the time required for the annealer to produce that solution.

[1] Daspal A, Das O. (2025). QUBO Formulation for Task Offloading in Mobile Cloud Computing. IEEE International Conference on Quantum Computing and Engineering (QCE25), Extended Abstract, 404-405.

Skills required:
Strong skill:Python Programming, Mathematical Optimization
Good skill: Linear Algebra, Probability Theory
Optional skill: Basic quantum computing knowledge is an asset.

Research area: My research interest lies at the interface of the theory and application of deterministic optimization methods to problems in energy, transport and manufacturing. More precisely, I develop and implement exact and heuristic algorithms for solving integer and mixed integer optimization problems applied in the above industries

Student roles:
This project aims to extend a previously developed deterministic optimization model toward a stochastic operational framework capable of addressing uncertainty in drinking water distribution systems. By integrating scenario-based demand variability into real-time energy management strategies, the proposed research seeks to improve operational resilience, energy efficiency, and sustainability

Skills required:
Linear algebra; Mathematical optimization; Integer programming; Machine learning; Probability theory

Research area: My specialized research area is applied mathematics and mathematical biology, with a focus on dynamical systems, reaction–diffusion equations, pattern formation, and stochastic modeling. I study how complex spatial and temporal patterns arise in biological and physical systems, using tools from differential equations, asymptotic analysis, perturbation methods, stability theory, and numerical simulation. In particular, my research includes the analysis of nonlinear PDE and ODE models, epidemic and ecological dynamics, localized patterns such as spikes and mesas, and the effects of noise, domain growth, and adaptive feedback on pattern formation and stability.

Student roles:
The student will play an active role in developing and analyzing mathematical models for recurrent epidemic outbreaks. They will begin by learning the background of SIRS epidemic models, adaptive human behavior, evolutionary game theory, and viral evolution. This will provide the foundation for building extended SIRS-type models that include feedback between disease transmission, individual behavior, and possibly multiple viral strains or evolving viral traits.

I will mentor the student in carrying out mathematical analysis, including the study of equilibrium solutions, stability, and possible bifurcations that may lead to recurrent outbreaks. Numerical simulations will be used to support and guide the analysis. The student will implement the models in MATLAB, Python, or a similar platform, generate time-series simulations, explore parameter regimes, and compare stable, periodic, and more complex outbreak patterns. They will also prepare figures to illustrate the analytical and computational findings. I will also support the student in preparing figures that illustrate the analytical and computational findings.

Throughout the internship, I will meet regularly with the student to discuss mathematical ideas, interpret simulation results, and refine the model. I will also mentor them in key academic competencies, including mathematical modeling, critical thinking, numerical experimentation, and research communication. By the end of the internship, I will guide the student in summarizing the main findings in a short report or, depending on progress, a manuscript for publication.

Skills required:
The student should have a background in mathematics, applied mathematics, physics, engineering, computer science, or a related quantitative field. Basic knowledge of ordinary differential equations, numerical methods, and mathematical modeling would be helpful. Since the project involves simulations, some programming experience in MATLAB, Python, or a similar language is strongly preferred. Prior knowledge of epidemiological modeling, dynamical systems, or evolutionary game theory would be an asset, but is not required. The student should be curious, motivated to learn new mathematical and computational tools, and interested in applying mathematics to biological or public-health related questions.

Research area: My research lies at the intersection of mathematical optimisation, machine learning and mathematical modelling (in particular using probability theory).

Student roles:
The student will experiment with data and implement the RL algorithm. If the project progresses as planned, the work will contribute to a research article to be co-authored by the student.

The project will be co-supervised by Prof. Ana María Anaya-Arenas and take place at UQAM, the Centre de recherche mathématiques (CRM) and the Group d'études et de recherche en analyse de décision (GERAD). The student will be able to participate in scientific activities in this rich environment.

Skills required:
The student should have some background in reinforcement learning, ideally through a project (either in a course setting or through independent study).

Programming experience in Python is required, as the project is implementation-focused. Familiarity with inventory management or operations research is a plus but not required.

Research area: Topology is the mathematical study of spaces. My research area is algebraic topology, which describes the shape of spaces using algebraic quantities that we can compute. For example, topologists can tell apart a sphere from a torus (donut), using either the fundamental group or homology groups. My research concerns the extent to which such algebraic invariants determine a space, and about putting as much structure as possible on the algebraic invariants, in order to retain more information about the space.

Student roles:
The research intern will solve the following tasks.

1. Learn the basics about stable module categories, notably their triangulated structure.

2. Familiarize oneself with existing GAP code to compute maps in the stable module category.

3. Write code (in GAP or Sage) for further computations in the stable module category. The following features are desirable:
- Compute the cofiber of a map, that is, extend any map to an exact triangle.
- Test whether a candidate triangle is exact.
- Test whether two exact triangles are isomorphic.
- Compute all the cofiber fill-ins starting from a commutative square.

Skills required:
On the theoretical side:
- A course in linear algebra.
- A course in abstract algebra, e.g., group theory, rings, fields, and modules.

On the practical side:
- Some coding experience, in any programming language.
- Ideally some experience with mathematical software, such as GAP, Sage, Mathematica, or Maple.

Research area: I am professor in mathematics in the field of probability theory. My research focuses on the study of stochastic processes, their properties and long-time behavior. I am interested in models in various fields (physics, biology, actuarial science) involving processes such as piecewise deterministic Markov processes (PDMPs), interacting particle systems, diffusions, random walks, and Lévy processes.

Student roles:
The internship is structured in different stages: first, the student will explore the main question, then discover the literature on the subject and deepen their knowledge, so as to be able to develop new approaches and obtain new mathematical results. The student is free to propose and explore new avenues of research, with the support of the supervisor. The internship will take place at the Université du Québec à Montréal, in the Mathematics Department. The intern will be co-supervised with a postdoctoral student. Weekly meetings will be held to discuss progression of the project. In addition, the intern will interact with students and other interns in the department. A report will be written in Latex, in order to give an overview of the work carried out during the internship.

Skills required:
The student should have a mathematical background, with a good theoretical grounding in all areas of mathematics, especially in probability. Knowledge of convergence of sequences of random variables, Markov chains and martingales is an asset. Programming skills (in Python or R) are not required, but could be useful for illustrating mathematical results.

Research area: I am an assistant professor in the Department of Operations and Decision Systems of Université Laval. My research focuses on the (joint) application of optimization and machine learning in decision-making contexts for the development of state-of-art AI-based decision systems. My research interests are: 1. Optimization and operational research: combinatorial, mathematical, multiobjective optimization, heuristics, metaheuristics; 2. Metasimulation and machine learning: big data analytics, decision-making, interactions between optimization, simulation and machine learning; 3. Applications: humanitarian and industrial applications, business intelligence/analytics.

Student roles:
This project is an introduction to research in optimization. The student will act as a researcher on the project for the duration of the internship and will thus be given some autonomy. The problem tackled by the student will be challenging. Hence, a third year PhD candidate with strong knowledge of the project and expertise in combinatorial optimization will guide the student on a daily basis. Frequent meetings will be conducted with the professor to discuss the progress.

This internship is a great opportunity for students interested in developing their knowledge in the field of operations research. Important skills in research and mathematical modeling will be developed through establishing a methodology to gather data related to the research question and following mathematical modeling experiments. The student will be asked to adapt and compare relaxation techniques or to develop one of their own, hence requiring creativity. The student's research can lead to the writing and submission of a short scientific paper to an operations research journal. From a long-term perspective, the work of the student will provide strong insights to the research group for the further development of heuristic or exact algorithms.

The internship will be divided as follows. Weeks 1-2 will involve learning modeling techniques and languages within Python. Weeks 3-5 will involve a literature review and learning various relaxation methods. Weeks 6-8 will involve the design or adaptation of a relaxation method for the stochastic arc routing problem formulation provided by the professor. Weeks 9-10 will involve performing reproducible software experiments. For the remainder of the internship, the student is expected to discuss his findings in a report formatted as a short scientific paper in LaTeX.

Quebec city is a French-speaking city and Université Laval is a French-speaking university. The internship can be conducted in French or English.

Skills required:
The student is expected to have coding experience:
1. Fluency in Python is required.
2. Experience with C++ and LaTeX might be useful.

Experience in optimization is an important asset. Experience in one of the following is a must:
1. Constraint programming.
2. Mixed-integer linear programming.
3. Mathematical programming.
4. Convex optimization.
5. Applied mathematics.

The student must be willing to tackle problems using a variety of optimization techniques, including mathematical programming with solvers such as CPLEX, Hexaly, and Gurobi. The student must have strong mathematical skills.

General skills:
1. Environment: Linux
2. English: reading and writing

Research area: My research area is operator algebras, a branch of functional analysis within pure mathematics. The research project is not directly in operator algebras, but interfaces with it.

Student roles:
The student will study the research and work on problems related to it, meeting/presenting their progress weekly. The student will likely be partnered with another undergraduate student. The student will write a short report at the end of the research term.

Skills required:
Background in real analysis is mandatory: the student should be familiar with the concept of a metric space, compactness, and connectedness. Further background in analysis (e.g., knowing the definition of a topological space, total disconnectedness) is a bonus.

Research area: My research focuses on mathematical modeling and analysis of cancer immunotherapy and cellular signaling pathways. I develop various types of mathematical models to mimic the dynamics and interactions in the tumor microenvironment (TME) under different cancer therapies or to address specific biological questions. My modeling work involves both qualitative and quantitative studies. In cancer studies, we use model predictions to evaluate potential treatment strategies, aiming to design optimal personalized treatment protocols or identify biomarkers for therapies. For cellular signaling pathways, our works help filter hypotheses and identify unknown factors, and predict the behavior of mutations under specific stimuli.

Student roles:
Read and present the related experimental and/or modeling papers
2. Create mathematical models: PDE models (fixed or free boundary) or ODE models
3. Find experimental evidence to support the assumption of the models
4. Write the Matlab codes to generate the numerical solution for the created models
5. Perform the model calibration for data fitting
6. Numerical simulation
i) Model validation to the experimental data
Use the Matlab coding to generate accurate numerical solution and adjust the parameter values based on the experimental data, numerical outcome to provide the qualitative fitting. After having this result, the intern needs to explain the finding from the simulation in the Latex file and also create the high-resolution pdf files for these numerical results.
ii) Numerical prediction- synergy analysis / treatment protocol design
test different combinations of treatment dosages and schedule to generate a heat map for this synergy analysis.
iii) Sensitivity analysis
Use the Latin hypercube sampling to generate at least 10000 samples and then calculate their partial rank correlation coefficients (PRCCs) and p-value corresponding to the tumor outcome.
7. Bifurcation analysis
8. Analyze the dynamics of the model
9. Use Latex to write the manuscript for this project

Skills required:
1. Programming skills for Matlab
2. Modeling skills for ODE or PDE models
3. Know how to generate numerical solutions for ODE or PDE model by using Matlab
4. Willing to learn some biological data / background
5. Analysis skills for ODE model, including existence, uniqueness, and boundedness of solution, positive invariant set, local stability of equilibria, bifurcation analysis
6. Use Latex for manuscript editing

Research area: Tensor, also known as super-matrix, is one of the important research objects in algebra. A matrix can be regarded as a two-dimensional tensor, but the research on tensors of three dimensions and above is far more difficult and complex than matrices. Most computational problems in tensor research are NP-hard. Tensors have a long history of research and wide applications: from early Einstein's general theory of relativity to recent fields such as data mining, neural networks, machine learning and image processing.

Student roles:
In my research work, there are a lot of algorithms which have to be implemented in mathematical software MatLab. I need to use these algorithms to compute and test some hypothesis, show the efficiency of the algorithms and also use them to compare my results with others. During the first two or three weeks, students will learn some MatLab programming skill and necessary mathematical background related to my project. After that, students will start to design/implement/test algorithms, and analysis results. They will work with my current research team including graduate students and undergraduate summer research students. Learning the design and implementation of algorithms will provide high quality training for the students.

Skills required:
Students have already taken some advanced algebra courses. Computer programming skill is preferred but not required.

Research area: Topology is the mathematical study of spaces. My research area is algebraic topology, which describes the shape of spaces using algebraic quantities that we can compute. For example, topologists can tell apart a sphere from a torus (donut), using either the fundamental group or homology groups. My research concerns the extent to which such algebraic invariants determine a space, and about putting as much structure as possible on the algebraic invariants, in order to retain more information about the space.

Student roles:
The research intern will solve the following tasks.

1. Learn the basics about dg-algebras, dg-modules, and their homology.

2. Familiarize oneself with software that computes the homology of chain complexes (e.g. using Sage). Work out some examples.

3. Write code to compute the homology of a dg-algebra, including its structure of graded algebra.

Skills required:
- A course in linear algebra.
- A course in abstract algebra, e.g., group theory, rings, fields, and modules, commutative algebra, or homological algebra.
- Ideally some experience with mathematical software, such as Sage, GAP, Mathematica, or Maple.

Research area: Bayesian statistical analysis, Statistical decision theory, Applied probability, Multivariate statistical analysis

Student roles:
Background preparation on order statistics and prediction. Analytical work on Bayesian modelling, inference and prediction. Implementation and coding. Applications to actual data sets. Summary of results. Wirtten summary.

Skills required:
Good knowledge in mathematical analysis, Bayesian analysis, statistical inference and probability. Expertise in mathematical programming.

Research area: My research background lies in algebra and representation theory, but I am currently moving towards applications of these areas, such as in topological data analysis (TDA). TDA seeks to find structure in large data sets using methods from topology, such as computing homology groups. It has been applied to detect important features in numerous applications ranging from medicine to cybersecurity. Much of the recent progress in TDA is based on the study of persistence modules, and this is where my expertise in algebra can be applied. My recent preprints can be found on arXiv here: https://arxiv.org/search/math?searchtype=author&query=Brüstle

Student roles:
For a three months project, the first month will be devoted to learn: what is the goal of the project, what are pertinent literature and existing methods and software. The second month will be dominated by applying these previously acquired methods to the main question. This can be experimental (like testing on a computer if one can find more efficient methods in computing persistent modules and estimating the rank invariant) or theoretical (apply results from algebra to establish stability results).

Skills required:
A good knowledge of linear algebra is required, as well as ability to implement and test new or existing methods on a computer. Experience in advanced courses such as tolopogy or homology would be great but is not required. Also, experience in numerical or stochastic methods in computing would be an asset.

Research area: Computational Mathematics, Inverse problems, Scientific Computing, Numerical Analysis, Modelling, Deep Learning, Full Waveform Inversion.

Student roles:
The student will be a hands-on research contributor responsible for the implementation and experimentation at the core of the project. Specifically, they will:
(1) Prepare and explore data, loading and visualizing the breast phantoms and their paired wave simulations, and understanding the USCT acquisition setup.
(2) Implement and train the neural network surrogate for the acoustic wave equation, starting from a baseline architecture and iterating on the physics-informed training objective under supervision.
(3) Integrate the surrogate into the FWI loop, replacing or augmenting the conventional numerical solver, and getting the end-to-end reconstruction pipeline running.
(4) Run experiments and evaluate results, comparing reconstruction accuracy, computational speedup, and robustness against conventional solver-based FWI and existing baselines.
(5) Document and communicate, keeping a reproducible record of code and numerical experiments, and presenting progress in regular meetings, culminating in a written report or poster (and potentially contributing to a publication).

Skills required:
(1) Programming in Python or Matlab or C/C++. Comfortable writing and debugging non-trivial code, using NumPy/SciPy. Experience with TensorFlow or PyTorch is helpful.
(2) PDEs, Numerical optimization, multivariable calculus and linear algebra, deep neural networks.

Research area: As described on my page https://freakonometrics.github.io/, the themes addressed in the work of students under my supervision are primarily focused on understanding and modeling risks, and actuarial models (or predictive models, more generally). Applications range from modeling climate risks to analyzing discrimination and equity. The models are primarily mathematical and require a solid foundation in mathematics, statistics, game theory, probability, or quantitative economics.

Student roles:
The student will have the option to:
(1) conduct a scientific literature review on a specific field
(2) work on a theoretical paper related to those issues

Skills required:
As mentioned previously, the student will need to have a strong foundation in mathematics, statistics, game theory, probability, programming, or quantitative economics. The direction of the topic will be tailored to take into account the student's strengths. The student must be able to read scientific literature in English.

Research area: My research is in physics-based animation, the branch of computer graphics concerned with simulating the motion of physical systems like deformable solids, cloth, fluids, and the contact between them. The work sits at the intersection of continuum mechanics, numerical optimization, and high-performance computing: we discretize the governing equations of motion, design solvers that are stable and fast under large time steps, and balance physical accuracy against the interactive performance that graphics applications demand. PhySherGraph, an in-house simulation framework, serves as the common platform for these projects, which lets interns build onto rather than start from scratch.

Student roles:
The intern will generate the GPU tetrahedralization pipeline from research to working implementation. The first weeks are devoted to studying the relevant literature, including jump flooding for distance fields, lattice-based and isosurface-stuffing approaches to tetrahedral meshing, and the mesh-shader programming model, and to familiarizing themselves with PhySherGraph's existing rendering and simulation infrastructure. With that grounding, they will design the pipeline's stages: surface voxelization, the jump-flooding distance-field pass, and the mesh-shader element-generation stage that emits tetrahedra.

Implementation proceeds incrementally and is validated at each step. The student will first produce a correct distance field, then a basic interior tetrahedralization, then boundary-conforming elements, checking mesh quality metrics against established baselines as they go. Once the generator runs, they will couple its output to our soft-body solver and verify that the resulting simulations are stable, profiling to remove bottlenecks. Throughout, they are responsible for clean, documented, reusable code that follows the lab's conventions.

The intern will work on a shared codebase at the heart of my team. They will have regular meetings with me, with the lab members, and develop communication skills leading to potential graduate research. By the end of the 12 weeks, the student will deliver a documented GPU tetrahedralization module, a quantitative evaluation of its mesh quality and runtime, and a short written report suitable as the seed of a research paper, a genuine and self-contained research contribution that previews graduate study in my group.

Skills required:
Strong C++ and hands-on GPU programming experience are essential, ideally with modern graphics APIs (Vulkan, DirectX 12, or WebGPU) and compute shaders; exposure to mesh shaders or the jump flooding algorithm is a strong asset but can be learned during the internship. The candidate should have a solid foundation in linear algebra, computational geometry, and 3D mathematics, and be comfortable reading and extending a substantial existing codebase. Coursework or projects in computer graphics, GPU computing, or geometry processing is highly valued. No prior physics-simulation experience is required. I will provide the necessary background in soft-body animation.

Research area: Our lab develops physics-informed neural networks for disease modelling and scientific machine learning. A recurring technical challenge across all our projects is gradient conflict in multi-objective training, where different loss terms produce update directions that disagree and stall the optimizer. We have recently developed an adaptive method to manage this conflict, but diagnostic tools for visualizing and understanding training dynamics in multi-task settings remain underdeveloped across the scientific machine learning community. This project focuses on building such tooling, and therefore contributes to research infrastructure at the intersection of scientific computing, machine learning, and open-source software development.

Student roles:
The intern will serve as lead developer on an open-source scientific software tool within the DIMMS Lab. The role combines software engineering with research applications and is ideal for a student who enjoys designing clean APIs, writing documentation, and producing polished code. During the first two weeks, the intern will onboard by reviewing our existing PINN codebase, studying representative training dynamics from our published experiments, and drafting an initial API design for the library. The intern will also survey existing tooling in the scientific machine learning community to identify gaps this library should fill. From weeks three to six, the intern will implement the core functionality including gradient hooks, cosine similarity computation, per-layer conflict metrics, and adaptive weight logging. Development will follow standard software engineering practices including version control, unit testing, and continuous integration. Weekly meetings with the supervising team will guide API decisions and prioritize features. From weeks seven to nine, the intern will build the visualization layer, including real-time plotting, training-run summaries, and publication-quality figure export. The intern will validate the tool on two to three PDE benchmarks from our lab's codebase. During weeks ten to twelve, the intern will write comprehensive documentation, create example notebooks demonstrating the tool on real research problems, package the library for distribution on PyPI, and draft a short software paper for submission to the Journal of Open Source Software. The intern will present the tool at a final DIMMS Lab seminar. The intern will work independently on most development tasks but will collaborate closely with the PhD student and other lab members on API decisions and testing. All code will be released publicly. The intern will be listed as lead developer and co-author on the software paper.

Skills required:
Undergraduate standing in Computer Science, Software Engineering, or a related discipline (third or fourth year preferred). Strong Python programming skills are essential, along with solid experience using PyTorch. Familiarity with matplotlib or similar visualization libraries is required. Experience with Python package development (pip, setuptools) or open-source GitHub workflows is a strong asset. Interest in scientific computing, research tooling, or machine learning infrastructure is important. No background in differential equations or physics is required for this project; the focus is primarily on software design and development.

Research area: Our group develops learning-augmented optimization deployed at industrial scale (airlines, airports, mining). We are opening a rigorously evaluated quantum direction: where, if anywhere, do quantum and quantum-inspired methods help solve operational combinatorial problems? With quantum-computing collaborators at Concordia and access to cloud quantum hardware through Québec's quantum ecosystem (PINQ²'s utility-scale 127-qubit IBM Quantum System One; Calcul Québec), we study hybrid quantum-classical pipelines against honest classical baselines, producing the evidence the field currently lacks.

Student roles:
The intern works with weekly 1:1 supervision, co-mentored by a quantum-computing graduate researcher in the group and our solver-focused PhD students (a large, active lab where several members work on adjacent solver and benchmarking problems). The intern owns the pipeline in stages: problem encodings and classical baselines first, then the hybrid and quantum-inspired algorithms with simulator and cloud-QPU experiments. Weeks 1-2: literature and tooling onboarding (Qiskit/PennyLane, our solver stack). Weeks 3-5: encoding library and baseline harness; first QAOA runs. Weeks 6-9: benchmark grid across problem families, sizes, and compute budgets; embedded-oracle experiments. Weeks 10-12: scaling analyses, the "quantum readiness map", open-source release, and a co-authored manuscript draft; final presentation to the group. Deliverables: encoding library, benchmark suite with leaderboard, and manuscript. Strong interns continue remotely toward publication and are well placed for graduate positions as our quantum-for-operations line grows.

Skills required:
Strong Python; solid linear algebra and probability; coursework in quantum computing or hands-on exposure to Qiskit/PennyLane (a quantum summer school or hackathon counts); optimization basics (MILP, local search). Rigor and intellectual honesty matter most: this project rewards students who value verifiable evidence over hype. Physics, mathematics, and computer science backgrounds all work here; olympiad-style problem solving is a plus.

Research area: Since July 2021, Nadia Tahiri has held the position of Assistant Professor in the Department of Computer Science at the Université de Sherbrooke. Her research program primarily focuses on enhancing our understanding of the mechanisms responsible for biodiversity generation and maintenance. Specifically, she is dedicated to identifying evolutionary processes and developing new criteria for this purpose. Throughout her career, she has undertaken various projects, including the creation of a rapid and reliable method for detecting and confirming horizontal gene transfer events using phylogenetic trees. She has also designed a phylogeographic approach to study the diverse species of wild coffee in

Student roles:
We are currently engaged in the development of the initial version of aPhyloGeo (analysis phylogeography). Interns will play a crucial role in various tasks to advance the project.

1. The interns will contribute to the development of a web platform that supports the concurrent analysis of multiple users. The objective is to create a platform that allows for seamless collaboration and fosters healthy competition among users, enhancing the overall research experience.

2. To ensure efficiency and maintainability, optimizing the source code will be a priority. This will involve documenting the code thoroughly, ensuring clear explanations of the implemented processes, and promoting code accessibility. These efforts will enable easy understanding and future enhancements by both current and future contributors.

3. To further enhance performance, interns will work on code parallelization and the deployment of the software on a dedicated server. By leveraging parallel computing techniques and efficient resource allocation, the system's capabilities can be significantly improved, allowing for faster and more efficient data processing.

4. A crucial aspect of the project will be on designing and implementing an advanced algorithm capable of simultaneously analyzing genetic and climate data. This algorithm will enable a comprehensive understanding of the intricate interplay between genetic factors and climatic influences in the context of phylogeography.

Through these intern-driven tasks, we aim to create an advanced and comprehensive tool for phylogeographic analysis. The collaboration of interns will play a significant role in shaping the future of aPhyloGeo, making it a valuable resource for researchers in the field.

Skills required:
The ideal candidate should possess strong programming skills in languages such as C, C++, Python, as well as proficiency in web languages like CSS and JavaScript. Knowledge of algorithms and graph theory is desirable. Familiarity with bioinformatics would be an added advantage. The student should be highly independent, proactive, and able to work autonomously. Fluency in both written and spoken English or French is required.

Research area: Since July 2021, Nadia Tahiri has held the position of Assistant Professor in the Department of Computer Science at the Université de Sherbrooke. Her research program primarily focuses on enhancing our understanding of the mechanisms responsible for biodiversity generation and maintenance. Specifically, she is dedicated to identifying evolutionary processes and developing new criteria for this purpose. Throughout her career, she has undertaken various projects, including the creation of a rapid and reliable method for detecting and confirming horizontal gene transfer events using phylogenetic trees. She has also designed a phylogeographic approach to study the diverse species of wild coffee in

Student roles:
We are currently engaged in the development of the initial version of iPhyloGeo (interactive phylogeography). Interns will play a crucial role in various tasks to advance the project.

1. The interns will contribute to the development of a web platform that supports the concurrent analysis of multiple users. The objective is to create a platform that allows for seamless collaboration and fosters healthy competition among users, enhancing the overall research experience.

2. To ensure efficiency and maintainability, optimizing the source code will be a priority. This will involve documenting the code thoroughly, ensuring clear explanations of the implemented processes, and promoting code accessibility. These efforts will enable easy understanding and future enhancements by both current and future contributors.

3. To further enhance performance, interns will work on code parallelization and the deployment of the software on a dedicated server. By leveraging parallel computing techniques and efficient resource allocation, the system's capabilities can be significantly improved, allowing for faster and more efficient data processing.

4. A crucial aspect of the project will involve designing and developing an interactive and user-friendly dashboard. This dashboard will serve as a central hub for task processing, providing intuitive controls and real-time updates. By creating an engaging and accessible interface, users will have a streamlined experience while managing their tasks within the iPhyloGeo platform.

Through these intern-driven tasks, we aim to create an advanced and comprehensive tool for phylogeographic analysis. The collaboration of interns will play a significant role in shaping the future of iPhyloGeo, making it a valuable resource for researchers in the field.

Skills required:
The ideal candidate should possess strong programming skills in languages such as C, C++, Python, as well as proficiency in web languages like CSS and JavaScript. Knowledge of algorithms and graph theory is desirable. Familiarity with bioinformatics would be an added advantage. The student should be highly independent, proactive, and able to work autonomously. Fluency in both written and spoken English or French is required.