Current DRP Projects

Mentor: Zoya Abbasi

Mentees: Paige Li and Zunairah Shahzad

Description: 

Curious about how we predict the spread of diseases like COVID-19? Our project uses math to build models forecasting infection trends, testing solutions like vaccines, and shaping health policies. You’ll get hands-on experience creating and analyzing these models to help protect communities—no advanced math is required! Join us to see how math can tackle real-world health challenges!

Mentor: Mohsen Rezaeian

Mentees: Victoria Kolb, Georgina Wang, Lily Jiang and Siri Sujay

Description: 

Cancer is a complex disease, and studying it requires tools that can capture this complexity. One important area of cancer research focuses on chemotherapy—the process of delivering drugs to tumour sites to kill cancer cells. In this project, we bring together three powerful approaches: mathematical modelling (using equations to describe how drugs travel through the body and reach solid tumours), machine learning (a type of artificial intelligence that finds patterns in data), and tumor-on-a-chip systems (tiny lab devices that mimic the tumour’s microenvironment). By combining these methods, we aim to better understand how chemotherapy drugs move through tissues, interact with cancer cells, and how treatment effectiveness can be improved. In this learning opportunity, students will explore how these three cutting-edge tools are used to study and improve cancer chemothrapy.

Mentor: Hassaan Qazi 

Mentees: Christina Zijun He and Bandana Bajaj 

Description: 

In this study, we will investigate how to apply graph-theoretic tools to achieve consensus and formation control of a swarm of flying drones. We will start with the fundamentals of graph theory and will read some literature available on the coordination and cooperation of Unmanned Aerial Vehicles (UAVs). To make the project more realistic, we will impose assumptions on the agents' communication capacity with the centralized control hub. Furthermore, we will try to incorporate the strategies to deal with the delays that happen in the communications and prepare the overall scheme for fault tolerance. The emphasis will be to design a control law that tracks the time-varying target.

The project has a wide range of applications from monitoring the environment in agriculture to capturing images of airplanes from various angles in the aeronautics industry.

Mentor: Zaheer Mohideen

Mentees: Andrea Lagunes Betanzos, Isabella Wang

Description: 

Osteoporosis, a condition where bones become brittle and break easily, affects one in four women over 50 due to age-related changes in the balance of calcium. In this project, we will explore how the body maintains calcium homeostasis using an ordinary differential equation (ODE) based mathematical model. Focusing on a female rat model, we will simulate how factors like aging, diet, and medication like osteoporosis treatment affect calcium, vitamin D, and bone activity. Most simulations will be done in MATLAB, so prior experience is recommended. No prior biology knowledge is required — just curiosity and an interest in mathematical modelling!

Mentor: Rian Neogi

Mentees: Anika Smith, Saransh Jindal and Stella Xiao

Description: 

Consider the following tasks: (1) Design a road network in a city that minimizes traffic congestion, (2) Design a procedure to allocate a set of goods from potential sellers to potential buyers, (3) Design an algorithm to match DRP students to DRP mentors. All these tasks have one thing in common: They involve dealing with strategic agents whose goals differ from one another. In (1), people choose a route to their destination that is the shortest, even if it increases congestion. In (2), sellers and buyers may choose to over-report or under-report the value of items, if they find that it improves their net gain. In (3), it is desirable that a student and a mentor do not prefer each other over their assigned candidate. Algorithmic Game Theory involves design procedures in settings with self-interested strategic agents. We will first cover the basics of the field and then dive deeper into a subfield of your interest, potentially even designing our own procedure for an AGT setting.

Mentor: Maryam Mohammadi Yekta

Mentees: Danielle Rodgers and Erin Guerard 

Description: 

A multivariate polynomial can be represented by its coefficients, roots, or evaluation function. The connections between these three ways of  representing a polynomial have been studied for many years in mathematics.

Recently, this machinery has been used in computer science and combinatorics as follows: Given a mathematical object A, we can encode A in a polynomial p, say by looking at its generating polynomial. We can then study how the properties of p help us prove statements about A. For instance, log-concavity of the function value of these polynomials has proven to be a useful tool to solve longstanding problems about the underlying objects. The Kadison-Singer, sensitivity, and Mason's conjectures are examples of problems solved using this method.

In this project, we will explore various classes of log-concave polynomials. We will study their structure and how they can be used to prove combinatorial results.

Mentor: Xinyue Fan

Mentees: Heer Mehta and Evan Rosen

Description: 

The Hadwiger's conjecture is one of the most challenging conjectures in graph theory. It generalizes the Four Color Theorem, and relates  In this project, we will learn about what it is, what makes it so challenging, why people are so obsessed with it, and maybe some relaxations of it that were proven to be true.

Mentor: Shanza Shanza

Mentees: Na Peng, Shu Cong and Yizhou Lou

Description: 

This project explores how families from diverse cultural backgrounds in Canada, particularly those from immigrant communities, navigate digital privacy and security when sharing devices at home. It aims to understand the social, cultural, and economic factors influencing their experiences and to support the development of more inclusive and accessible privacy solutions that reflect their everyday realities.

Mentor: Layth Ali Al-Hellawi

Mentees: Leon Yang, Gloria Jianan Wang and Taiqian Zhang

Description: 

A lot of research in algorithms-focused research in any math discipline often circles the Millenium Prize problem: does P = NP? These problems often emerge in practice when we codify a difficult problem that where we can brute-force all our possibilities, but there's a barrier of difficulty when we try and consider making more efficient algorithms. In the first third/half of the semester, we will focus on reading "Computational Complexity: A Modern Approach" (Arora, Barak) to formalize P and NP.

Nonetheless, we are still interested in the solutions for NP-Hard problems! So instead, we consider efficient approximation algorithms. We analyze both their level of efficiency as well as how close they are to actual solutions, in the worst case. For these, we read "Approximation Algorithms" (Vazirani) to learn about approximation algorithm construction and analysis. While I would like to focus on part 2 with LPs and SDPs, students can feel free to read about what algorithms interest them.

Mentor: Vyom Patel

Mentees: Caroline Knoke and Susie Cao

Description: 

With global efforts ramping up in quantum technology, learning the foundations of quantum computing gives you a head start in one of the fastest-growing fields. In this project, you'll explore quantum computing with just a background in linear algebra. Using ZX calculus, a visual, user-friendly method to represent quantum operations, you'll learn how quantum computers work and how they differ from regular ones, all while using intuitive diagrams that make complex concepts easier to grasp.

Mentor: Kaleb Domenico Ruscitti

Mentees: Alex Palmer, Mathilda Lee and Simran Matharu

Description: 

Over the last decade, large language models have become a hot and controversial topic. Some people believe we are on the cusp of creating artificial intelligence. On the other hand, some people are skeptical that these models are really "learning" anything at all.

Machine interpretability is the area of research dedicated to studying how we can interpret what machine learning algorithms are doing. Mechanistic interpretability attempts to do that by reverse-engineering trained neural-networks.

In this project, I want to try to understand and replicate the experiments found in the paper "Progess Measures for Grokking via Mechanistic Interpretability" by Nanda et al. In the paper, they train a neural-network to perform modular arithmetic and try to interpret the result. They claim the neural network has learned to do modular arithmetric using  "discrete Fourier transforms and trigonometric identities to convert addition to rotation about a circle." Let's try to see it for ourselves!

Mentor: Vecna

Mentees: Melanie Foltak, Sarah Nurse and Xinyi Chen

Description: 

When we talk to our friends using technologies such as SMS or Internet-based messaging apps, third parties such as corporations and governments can learn a lot about us. They can almost always learn who our friends are, and they can frequently even read our private messages! In this project, we will explore different technologies for private messaging. Topics may include encryption protocols, key verification, and metadata protections.

Mentor: Yiran Hu

Mentees: Jiarui Han and Eileen Wen 

Description: 

This project primarily focuses on evaluating and improving the fairness of language models. At present, an increasing number of language models are being applied in daily life, but the biases introduced by language models cannot be ignored. For example, language models may exhibit gender bias during interactions with humans. When I ask a language model about nurses, it is more likely to use "she" as a pronoun rather than "he." Additionally, related studies have shown that language models may also display career bias, location bias, and other types of biases when addressing real-world problems. If these issues are not evaluated and mitigated, they could pose significant risks to the application of language models in daily life. This project will guide students in understanding and exploring the fairness issues of language models, and provide them with an initial introduction to research work aimed at addressing these challenges.

Mentor: Gengyi Sun

Mentees: Lily Li, Bhavya (Bhavya) Modi, Anwesha Bali and Deepika Anbalagan

Description: 

To manage the development process of complex software, build systems are widely adopted to perform routine checks after code submissions. While build systems provide numerous benefits, the rapid pace of modern software development generates heavy workloads for them to process. Especially when a build fails, the consequences ripple throughout the development process.

Failures not only block others from validating their work but also necessitate repeated executions, incurring more resource consumption. Such inefficiencies contribute to wasted computing resources and energy and hinder productivity, emphasizing the need for more cost-effective solutions.

By leveraging machine learning approaches, we could assist developers in automatically re-implementing the failed test cases to fix the build failure.

This project aims to brainstorm methods to automate and accelerate the build repair process.

Mentor: Faisal Romshoo

Mentees: Chandni Wadhwa, Margaret Puzio and Khushi Adukia

Description: 

In your mathematical journey so far, you may have encountered the standard cross product in the three-dimensional space that we all live inside of. You take two vectors in three-dimensional space, take their cross product and obtain another vector which is perpendicular to both the original vectors. Turns out, that this is not the only cross product out there. We can also define a vector product on seven-dimensional space which is known as the exceptional cross product. We will learn about this cross product and how it leads to very interesting geometries.

Mentor: Jashan Bal

Mentees: Helen Wei, Megan Winterburn and Yanna Jaskielewicz

Description: 

Often times combinatorial results like the Ramsey theorem, Hales-Jewett, and Van der Waerden's theorem have quite complicated and long proofs. However, the above results can also be proved using abstract analytic methods. Often times the analytic proof is much shorter and more concise! The aim of this project is to understand these finite combinatorial results using analysis.

Mentor: Michelle Molino

Mentees: Chelsea Kim, Changhong Li, Tamar Gendler and Jessica Ni

Description: 

The p-adic numbers were invented by Kurt Hensel in the late 1800s as a new way of thinking about numbers—and they turned out to be incredibly useful. These numbers behave in strange and interesting ways, and today they're a key tool in number theory, cryptography, and more. In this project, you’ll get a feel for how p-adic numbers work, what makes them different, and why mathematicians care about them.

Mentor: Faisal Al-Faisal 

Mentees: Xing Liu and Emily Wang

Description: 

Elliptic curves lie at the intersection of different areas of mathematics. In popular (mathematical) culture, they're famous for being involved in the proof of Fermat's Last Theorem and for playing a role in mathematical cryptography. In this project, you will learn what elliptic curves are, where they came from, where they're going, and—most importantly—why they're so interesting!

Mentor: Roger Gu

Mentees: AJ Carson, Irene Chung and Cynthia Zhang

Description: 

The world is governed by differential equations—from Newton’s laws to models of heat, sound, and fluid flow. In calculus, you've seen tools like derivatives and integrals, but real-world solutions are often not smooth—sometimes not even continuous. In practice, many computational algorithms are used to approximate solutions to these equations—but why do these methods make sense? How can we rigorously understand such equations and their solutions?

In this project, we’ll explore Sobolev spaces, a framework that lets us make precise sense of “rough” solutions. We'll examine how much of calculus still applies and when it breaks down. If time permits, we'll apply these ideas to study properties of parabolic partial differential equations, and how this theory supports the algorithms commonly used to approximate solutions.

An analysis background is helpful but not required—just bring curiosity and a desire to see how formal math underpins practical problem-solving.

Mentor: Sita Gakkhar

Mentees: Cristian Moretto, Bowen Dai and Kris Zhang

Description: 

Automated theorem proving deals with formalizing mathematics so results can be verified using computers. Additionally, it makes it possible to use machine learning methods to search for proofs of conjectures and to find theorems bridging different parts of math. This reading is meant to tap into the anticipated usefulness of machine learning to accelerate mathematical research by introducing Lean, an automated theorem proving system and a functional programming language. Terry Tao (at UCLA) in his blog, https://terrytao.wordpress.com/2025/05/31/a-lean-companion-to-analysis-i/ has put forward a project to formalize his analysis textbook, Analysis I, using Lean. The goal for this term’s reading is to come up to speed with Lean, and following Terry’s lead, hopefully start contributing to the github repository for the project https://github.com/teorth/analysis . Time permitting we will attempt a Lean implementation to go along with Sussman et al’s text “Functional Differential Geometry.”

Mentor: Kyu Min Shim

Mentees: Drishti Handa and Jie Yang

Description: 

What if you could test hypotheses faster—stopping early when the answer becomes obvious? The Sequential Probability Ratio Test (SPRT) is a method developed in WWII to dynamically make decisions as you collect your samples. Today, it powers A/B tests of tech giants and clinical trials for new drugs.

In this project, you’ll: 1. Simulate SPRT (e.g., ‘Is this medication effective?’ or ‘Does this feature improve clicks?’); 2. Race it against traditional tests—see how SPRT often cuts sample sizes in half compared to the traditional fixed-sample tests, and; 3. Code a live demo in Python/R (no advanced math, just stats intuition!).

By the end, you’ll understand why tech giants and scientists rely on sequential testing. Perfect for stats/data science students who want to merge theory with real-world impact!

Mentor: Hao Quan

Mentees: Gabrielle Wu, Xinyi Nie and Violet Song

Description: 

We’re building a smart system that can predict the prices of different financial assets—like stocks, gold, and currencies—at the same time using a technique called multitask learning. This helps the model learn more effectively by finding patterns shared across markets. The project is a hands-on blend of finance, data analysis, and AI. You’ll work with real-world financial data using Python, and a basic background in machine learning or programming is preferred.

Mentor: Rhoda Dadzie-Dennis, Minh Chau Nguyen

Mentees: Shreya Jain, Suneet Kaur Mahal and Milagro Chen

Description: 

This project explores the impact of climate risk on both the asset and liability sides of financial products.

On the asset side, students will learn to build climate-resilient portfolios using tools from modern portfolio theory. They will integrate climate proxies such as carbon intensity, ESG scores, and Disaster Risk Index (DRI) metrics into portfolio models to assess how these risks influence investment decisions.

At the same time, the project examines how climate change impacts the liability side of financial products like insurance, pensions, and catastrophe bonds. For example, increased extreme weather events raise claims in Property & Casualty (P&C) insurance, while shifts in temperature may alter mortality and morbidity in Life and Health insurance.

Depending on students' interest, readings and exercises may focus on either P&C or Life. Topics like Extreme Value Theory or Generalized Linear Models may be introduced or reinforced based on students' background.

Mentor: Yan Yu

Mentees: Briana Peng and Iris Mo 

Description: 

Discover the fascinating world of hotel operations and customer experiences through data! In this project, you'll explore the exciting intersection of data science and business management by analyzing real-world hotel data. Gain valuable insights into customer behaviour, such as what influences their decisions and satisfaction, identify peak demand times to optimize hotel resources, and understand room availability issues that hotels commonly face. You'll also get hands-on experience with powerful predictive tools like LASSO and Random Forest models, learning how these methods help businesses anticipate trends and enhance operational efficiency. This project is perfect for undergraduates who are curious about how data-driven strategies shape business decisions and who want to develop practical skills highly valued in today's data-oriented industries.

Mentor: Joshua Joseph George

Mentees: Sri Meghana Yarlagadda, Madison Han, Chaozhong Wang and Parithy Senthamilarasan

Description: 

In this reading project, we will discuss some cool topics in probability theory. We will start with the basics in Probability (random variables, expected values, and moments) and cover the necessary content required for our readings. Since probability is all about studying uncertainty, we will explore this uncertainty and see how certain outcomes tend to concentrate around their expected values. This is done through the study of concentration inequalities. Then we will explore random matrices and even see how randomness shapes machine learning through concepts like Vapnik–Chervonenkis dimension. Students are expected to linear algebra, and calculus (should be comfortable with matrices, eigenvalues, eigenvectors, sums, series, integration, and differentiation). Some basic probability background, i.e, dealing with random variables and distributions, is preferred.

Mentor: Maryam Yalsavar

Mentees: Xena Jiang and Sandy Banh

Description:

Large language models like ChatGPT learn by focusing on the most important parts of text — this is called the attention mechanism. In this project, we will apply this same idea of "paying attention" to help computers solve partial differential equations (PDEs), which are mathematical tools used to describe things like how heat spreads or how fluids flow. By combining attention with these equations, we aim to create faster and more flexible ways to simulate complex systems in science and engineering.

Mentor: Harper Niergarth

Mentees: Vixail Hadelyn, Wenhui Li and Weiyou Li

Description: 

What do you get when you plug an integer partition into a symmetric function?

Given a partition λ, there’s a natural way to construct a new, larger partition f(λ) by evaluating a particular symmetric function—called an elementary symmetric function—on the parts of λ. Recently, an interesting question was asked: can two different partitions λ and μ give the same result, so that f(λ)=f(μ)? In this project, we will explore this question with the following twist: what happens if we replace “elementary symmetric function” with other kinds of symmetric functions? No prior experience with symmetric functions is required, we will build up the background together!

Mentor: Fernanda Rivera Omana, Noah Weninger 

Mentees: Richard Zhang, Elaine Zhao and Betty Zhang

Description: 

Verifying the correctness of mathematical proofs by hand can often be tedious and difficult. Using computer proof verifiers has increased in popularity in recent years, not only to check the correctness of new research but also as a teaching tool. Using proof assistants can help students learn mathematical rigour since the computer gives instant feedback on the correctness of the proof while it is being written. Lean4 is one of the most widely adopted proof assistant environments, and many results in graph theory have already been formalized in Lean4. However, many fundamental theorems remain to be formalized. One area where formalization of basic results is not complete is the study of Hamiltonian cycles. A Hamiltonian cycle of a graph is a cycle that covers all the vertices. The objective of this project will be to formalize results on Hamiltonian cycles in multigraphs.

Mentor: Matthew Hough, Viktor Pavlovic

Mentees: Eason Li and Qinyi Guo

Description: 

The Minimum Volume Ellipsoid (MVE) problem appears in data science and statistics. Given m points in R^n, the goal is to find the smallest ellipsoid that contains them all. This has practical applications in clustering, anomaly detection, and machine learning.

While the MVE problem is convex, solving it becomes computationally challenging as datasets grow. This project explores using the Primal-Dual Hybrid Gradient (PDHG) method—a fast, first-order optimization algorithm—to solve the MVE problem more efficiently.

Students will develop both the theoretical framework for applying PDHG to MVE and implement experiments to evaluate its performance compared to existing solvers.

Mentor: Alex Cowan 

Mentees: Sally Ann Hui, Peter Yang and Suhao Hu

Mentor: Jesse Huang

Mentees: Elizabeth Cai and Kenneth Xiao

Description: 

Investigate how the Kasteleyn matrix valued in Laurent monomials associated with a zigzag consistent dimer model on a torus changes as the zigzag paths deform in a Seiberg duality patterns or urban renewal moves.

Investigate how polynomial invariants of the Kasteleyn matrix change under these dimer transitions and prove that the associated toric Landau-Ginzburg models under dimer moves are related under cluster transformations of Laurent polynomials.

Mentor: Jingcheng Yu

Mentees: Nyra Rodrigues, Yurim Song, Cindy Yang and Wincy Huang

Description: 

We all make choices under uncertainty, whether it’s deciding if you should bring an umbrella, picking a new phone plan, or figuring out how much to save for a rainy day. But how do we actually think about risk—and how do banks, insurers, or even game designers use math to make sense of the unknown? In this project, we’ll explore the surprisingly fascinating world of risk and uncertainty. We’ll talk about real-life scenarios (no finance background needed!), dive into simple probability, and gradually build up to how these ideas power big decisions in finance and insurance. If you’re curious about why people play the lottery, how insurance works, or just want to see math applied in new ways, you’ll find something to enjoy here. Bring your questions and your curiosity—we’ll make sense of risk together!

Mentor: David Awosoga

Mentees: Anna Takegawa, Yushi Liu and Allie Dong

Description: 

Meta-analytics (Franks et al, 2017) can be used to evaluate the quality of metrics that are used to assess player ability in sports. This is important for effective comparisons to be made between them so that stakeholders are not overwhelmed with numerous metrics that lack practical significance, technical depth, or appropriate data considerations.

Meta-analytics are based on three criteria:

(1) stability: does the metric measure the same thing over time?

(2) discrimination: does the metric differentiate between players and

(3) independence: does the metric provide new information?

In this project we will apply meta-analytics to evaluate the quality and underlying properties of a set of volleyball metrics, so that we can identify those that provide the most unique and reliable information for the wider volleyball community, including coaches, athletes, and fans.