Past DRP Projects

Winter 2025 mentors and their projects

Project Mentors Mentees
1 (AM-Reading-1): How Math Unveils the Secrets of Infectious Diseases Like COVID-19 Zoya Abbasi Victoria Kolb, Xuanyi Chen
2 (AM-Reading-2): An Introduction to Quantum Computing through ZX Calculus Vyom Patel Emma Xing, Nicole Masodje
3 (AM-Reading-3): Parameter Estimation of the Hodgkin-Huxley Model Maxwell Yue Amy Bui, Debra Rose Defazio
4 (AM-Reading-4): Mathematical Modelling of Circadian Rhythm in Mammals Kaixin Zheng Yuan Yuan, Jackie Liu
5 (AM-Reading-5): An Introduction to Mathematical Climate Modelling Yusuf Aydogdu Joanna Jiang, Erica Han, Katrina Wohlgemut
6 (AM-Research-1): Efficient quadrature rules on two and three dimensional domains Zelalem Arega Worku Moustapha Diallo, Chloe Young, Shraddha Shankar Aangiras
7 (CO-Reading-1): Games on Graphs: Cops and Robbers Massimo Vicenzo Yuan Si, Silvia Zheng
8 (CO-Reading-2): Exploring Social Networks Through c-Closed Graphs Gabriela Bourla Jenna Johnston, Peter Yang
9 (CO-Reading-3): Introduction to Clique-Width Taite LaGrange Sarah Nurse
10 (CO-Research-1): Formalization of Tutte's linking theorem (Menger's theorem for matroids) Fernanda Rivera Omana and Mathieu Rundstrom Hadas Barabash, Jiaying Li, Nitya Kandadai, Zahra Ben Sabeur Tobar
11 (CO-Research-2): Past-future invariant and Causal Set Theory Kimia Shaban, Tiadora Ruza, and Ian George Hanyu Zhou, Alishba Malik, Lihuizi Chen, Jonathan Friedberg, Sherry Feng, Annie Sun
12 (CO-Research-3): Cutting-planes for Vehicle Routing Problems Matheus Jun Ota Modi Liu, Yirui (Ruby) Fang
13 (CO-Research-4): The interplay of Tyshkevich decomposition and other graph operations Cicely (Cece) Henderson and Hidde Koerts Boxuan Meng, Elaine Zhao, Helena Devinyak, Molly Wu
14 (CO-Research-5): Pick's theorem and its generalizations Jerónimo Valencia Porras Fillion Ding
15 (CS-Reading-1): Verifying Computation With Sum-Check Protocol Vahid Reza Asadi Rachel Ma, Vivian Guo
16 (CS-Reading-2): Mathematical Foundations of Deep Learning Juju Quartz Prisha Aggarwal, Abirami Karthikeyan
17 (CS-Reading-3): Probabilistic Methods in Computer Science Omkar Bhalchandra Baraskar Rachel Spanglet, Myra Gupta
18 (CS-Reading-4): Exploring Trade-offs in Mitigating Memory Vulnerabilities Ruizhe Wang Siyu Huang, Mikel Osei-Owusu
19 (CS-Reading-5): Exploring the usefulness of concentration inequalities to analyze randomized algorithms Prashant Gokhale Tanisha Dhami, Neva Wilson
20 (CS-Reading-6): Productive Curiosity Henry Yang Katherine Liu, Freya Zhang
21 (CS-Research-1): Serving Large Language Models on Budget GPUs Runsheng Guo Shu Cong, Maggie Liu, Divya Makkar, Anna Jia Wang
22 (CS-Research-2): Fully Encrypted Protocols Sina Kamali Lianghan Dong, Sarah Wilson, Stella Tian
23 (PM-Reading-1): Introduction to infinite structures Joey Lakerdas-Gayle Ellie Hamer, Gisele Huang
24 (PM-Reading-2): Playing with vector bundles Paul Cusson Edward Chang, Betty Zhang
25 (PM-Reading-3): An introduction to classical knot theory: How to tell the difference between twisted piles of string Robert Harris Isabela Souza Cefrin da Silva, Soumya Menon
26 (PM-Reading-4): Mean value of an arithmetic function Zhenchao Ge Chandni Wadhwa
27 (PM-Reading-5): Harmonic Analysis of Locally Compact Groups Aleksa Vujicic Ziyan Chen, Khanjan Soni
28 (PM-Reading-6): Understanding Geometric Objects With Computer Algebra System Erica Liu Jessica Ni, Bowen Dai, Xena Jiang, Adrina Esfandiari
29 (SAS-Reading-1): Predictive Models in Health Care Xianwei Li XinYi Ye, Jialu Sun
30 (SAS-Reading-2): Exploring numerical methods for option pricing Xipeng Huang Qianqian Wang, Micky Liu
31 (SAS-Reading-3): An overview of Bayesian statistics Yixing Zhao Xiaoyan Wang, Catherine McCulloch
32 (SAS-Reading-4): When the Numbers Lie: An Analysis into the Misuse of Statistics in Research Jessica Xu Mathilda Lee, Maria Khan, Parithy Senthamilarasan, Anika Smith
33 (SAS-Reading-5): Exploring Hotel Operations and Customer Behavior through Data Analytics Yan Yu Lily Li, Anwesha Bali, Yanqi Gao
34 (SAS-Reading-6): Portfolio Selection under Climate Change: Integrating Climate Risk in Investment Rhoda Dadzie-Dennis Joanna Moon, Arielle Chan, Jane Zhu, Lena Ye

Fall 2024
Project Mentor Mentees
AM-Reading-1 Optimal control for ordinary differential equations Ala' Alalabi Haiyan Zhu and Neha Munje
AM-Reading-2 An Introduction to Mathematical Climate Modelling Yusuf Aydogdu Adya Bhardwaj, Neva Wilson, and Sampoorna Prakash
AM-Reading-3 Numerical solutions of common differential equations in mathematical physics Milad Moshayedi Aaisha Pathan and Simran Matharu
AM-Reading-4 How Math Unveils the Secrets of Infectious Diseases Like COVID-19 Zoya Abbasi Gaurika Gupta and Yashila Barnwal
AM-Reading-5 Optimization Methods for Image Processing Phuong Dong Le Ha Dang Vu, Khoi Hoang, and Monica Trinh
AM-Research-1 Modelling epidemic spread of plasmids in microbial communities Aaron Yip Chenyi Xu and Tong Liang
CO-Reading-1 Mechanism Design and Algorithmic Game Theory Rian Neogi Daisy Li and Shu Cong
CO-Reading-2 Numerical Semigroups via Chicken McNuggets Harper Niergarth Heer Mehta and Margaret Puzio
CO-Research-1 Three-Uniform Hypergraph Gridwalking via The Tutte Polynomial Josephine Reynes Bandana Bajaj and Page Stone
CO-Research-2 Finding Combinatorial Specifications for Chord Diagrams Kimia Shaban and Tiadora Ruza Sherry Feng, Hanwu Zhou, Hope Appelmans, and Purev Batdelger
CO-Research-3 Cutting-planes for Vehicle Routing Problems Matheus Jun Ota Modi Liu and Yirui (Ruby) Fang
CO-Research-4 The interplay of Tyshkevich decomposition and other graph operations Cicely (Cece) Henderson and Hidde Koerts Boxuan Meng, Elaine Zhao, Helena Devinyak, and Molly Wu
CO-Research-5 Pick's theorem and its generalizations Jerónimo Valencia Porras Fillion Ding and Melody Tian
CS-Reading-1 Software Foundations Edward Lee Feng Xiang Ming and Solara Lin
CS-Reading-2 Simulating Fluids with Physics-based Animation Anchit Mishra Khanjan Soni and Yifei Wang
CS-Reading-3 Exploring Explainable AI Methodologies Julie Wojtiw-Quo Harbin Dhillon
CS-Reading-4 Evaluating The Efficiency and Security of Blockchain Consensus Models Shashank Joshi Radha Kotra, Kamakshi Sarvananthan, Lily Wang, and Rena Yang
CS-Research-1 AI in Software Engineering: Evaluating LLMs in SE Noble Saji Mathews Anusheh Atif, Kriti Sodhi, and Nina Zhang
CS-Research-2 Fully Encrypted Protocols Sina Kamali Lianghan Dong, Sarah Wilson, and Stella Tian
PM-Reading-1 Singularities of curves Jiahui Huang Emily Wang and Nayantara Gummalla
PM-Reading-2 Introduction to Lattices and Order Alec Gow Debra Rose DeFazio and Shichen Gou
PM-Reading-3 Free Groups and the Word Problem Nicolas Banks Micky Liu and Brenda Li
PM-Reading-4 Word Hyperbolic Group Aareyan Manzoor Kenneth Xiao
PM-Reading-5 Primality Testing and Factoring Algorithms Owen Sharpe Manal Wasif and Sri Meghana Yarlagadda
PM-Reading-6 The Abel-Ruffini Theorem: or why there is no general formula for the roots of polynomials Yash Singh AJ Carson and Nicola Ablett
SAS-Reading-1 When the Numbers Lie: An Analysis into the Misuse of Statistics in Research Jessica Xu Eike Zhao and Meerra Vasuthevan
SAS-Reading-2 Exploring Hotel Operations and Customer Behavior through Data Analytics Yan Yu Arwen Mao, Ellen He, Julia Wrona, and Rachel Tania
SAS-Reading-3 Deciphering Causality: A Primer on Causal Inference Xiaoya Wang Catherine McCulloch, Ivena Yeung, and Ridhika Madan
SAS-Reading-4 An Introduction to Survival Analysis Xianwei Li Alina Hu, Calista Kurniawan, and Maya Le

Spring 2024

Spring 2024 DRP Projects

Project Mentor Mentees
´¡²Ñ-1ÌýNumerical solutions of common differential equations in mathematical physics Milad Moshayedi Mincy Yang and Alice Qi
AM-2 An Introduction to Mathematical Climate Modelling Yusuf Aydogdu Mabel Luo and Daisy Li
´¡²Ñ-3ÌýEfficient attention for long sequences Yanming Kang Sachi Shah and Hadeya Ikram
AM-4 A Journey through the Physics of Space and Time Matheus Hrabowec Zambianco Sehar Durrani and Rem Dong
AM-5 Neural network-based stability analysis for dynamical systems Ruikun Zhou Gengyang Chen and Jiaren Yue
AM-6 How Math Unveils the Secrets of Infectious Diseases Like COVID-19 Zoya Abbasi Shiyi Liu and Alishba Malik
°ä°¿-1ÌýHelly's theorem in the plane and beyond? Mathieu Rundstrom Heer Mehta and Sneha Elavarasan
°ä°¿-2ÌýTyshkevich Decomposition of Graphs Cicely (Cece) Henderson Nitya Kandadai, Zahra Ben Sabeur Tobar, Boxuan Meng, and Elanie Zhao
CO-3 Non-constructive methods in combinatorics Sepehr Hajebi Anna Henderson and Gioia De Leonardis
CO-4 Introduction to Graph Products Hidde Koerts Bandana Bajaj and Khanjan Soni
CO-5 Playing Tic-Tac-Toe on Combinatorial Designs Tiadora Ruza Novel Peng and Joyce Chen
CO-6 An Introduction to Biased Graphs Xinyue Xie Neha Munje and Amy Bui
°ä³§-1ÌýMathCraft: The Tower of Hanoi Odyssey Punit Kunjam Sophia Zhu, Luna Wu, and Alia Cai
°ä³§-2ÌýEvaluating the Efficiency and Security of Blockchain Consensus Models Shashank Joshi Yidan Wang and Lily Jiang
CS-3 Synergizing Information Retrieval and Large Language Models for Retrieval-Augmented Generation Ronak Pradeep Diliara Kaniazova
CS-4 AI & Software Engineering: Exploring LLMs for enhancing SE workflows Noble Saji Mathews Helen Dong and Fion Zheng
°ä³§-5ÌýThe burning number of a graph and related problems Prashant Gokhale Shriya Kulkarni and Lynn Li

CS-6 Statistical data depth in deep learning: Application to out of distribution detection

Ananya's Slides |

Spencer Szabados Ananya Kumar and Zayaan Mulla
±Ê²Ñ-1ÌýWallpaper Groups AJ Fong Bethelhem Bezabeh and Melody Tian
±Ê²Ñ-2ÌýIntroduction to Elliptic Curves and Modular Forms Yash Totani Bryan Chen and Natalia Weber
±Ê²Ñ-3ÌýStructure Theory of Rings Liam McQuay Amelie Zhou and Manya Singh
PM-4 Introduction to Tensor Products Annie Li Sara Nayar and Marshall Cowie
PM-5 Lie Groups Keke Zhang Hope Appelmans and Hanwu Zhou
PM-6 Understanding Geometric Objects With Computer Algebra System Erica Liu Stephanie Penner and Stella Xiao
³§´¡³§-1ÌýCausal Inference: Mimicking Potential Outcomes on a Single Individual Henan Xu Xinyang Li, Tiffany Wang, and Zhige Chen
³§´¡³§-2ÌýWhat goes into a sustainable investment? Minh Chau Nguyen Aastha Hiten Kotecha
SAS-3 Exploring Hotel Operations and Customer Behavior through Data Analytics Yan Yu Claudia McComb and Charlotte Liu

³§´¡³§-4ÌýDeciphering Causality: A Primer on Causal Inference

Slides | R Code & Data Format

 Xiaoya Wang Shu Cong
SAS-5 Portfolio Selection under Climate Change Rhoda Dadzie-Dennis Aliard Jerome and Jingyan Ji

³§´¡³§-6ÌýIntroduction to Missing Data Problem in Health Data

 Yuliang Shi Shuha Sheikh

Winter 2024

Winter 2024 DRP Projects

Project Mentor Mentees
´¡²Ñ-1ÌýMathematical Modeling of Potassium Regulation Melissa Stadt Betty Zhang and Lily Zhou
AM-2 Introduction to Mathematical Model of Infectious Disease Athira Satheesh Kumar Alice Sun and Austin Zhu

´¡²Ñ-3ÌýDynamics of the Neural Network

 Liang Chen Natalia Manturowicz and Alicia Lin

°ä°¿-1ÌýRobust Combinatorial Optimization

 Matheus Jun Ota Crystal Zhou and Xinyue Fan
CO-2 Tyshkevich Decomposition of Graphs Cicely Henderson Helena Devinyak and Molly Wu
CO-3 Lattice-point Enumeration of Polytopes Jerónimo Valencia-Porras Gloria Wang and Melody Tian
CO-4 Anti-Ramsey Theory Fernanda Rivera Omana Grace Terhljan and Soumya Menon

CO-5 Primality Testing and Factoring Algorithms

Daniel's Presentation.pdf | Tengyi's Presentation.pdf | Jazlynn's Presentaion.pdf

 Owen Sharpe Daniel Ting Feng Liu, Tengyi Xu, and Jazlynn Leung

°ä³§-1ÌýIntroduction to running your own LLMs for story generation (or any other use case)

 Aisha Khatun Kun Zhu and Qi Fang
CS-3 Evaluating the Efficiency and Security of Blockchain Consensus Models Shashank Joshi Yuhan Wu and Ashley Ge
CS-4 Diving Into Privacy Enhancing Technologies Sina Kamali Keqing Wang and Weixin Huo
°ä³§-5ÌýAlgorithms for Big Data: Sublinear and Streaming Algorithms Vihan Shah Rachel Ma and Vivian Guo
CS-6 Machine Learning for Brain-Computer-Interfaces Lena Podina Akira Yoshiyama
°ä³§-7ÌýThe Graph Container Method and Applications in Algorithms Cameron Seth Aadila Ali Sabry
±Ê²Ñ-1ÌýIntroduction to Algebraic and Computational Geometry by Exploring Elliptic Curve Cryptography Kaleb D Ruscitti Elizabeth Cai and Avery Cormier
PM-2 An Introduction to Model Theory Aareyan Manzoor Alice Schroeder and Elysia Wang

±Ê²Ñ-3ÌýWhy does the golden ratio show-up in flowers?

 Jérémy Champagne Jackie Liu and Lydia He

³§´¡³§-1ÌýIntroduction to Bayesian Inference

 Yiran Wang Keeley Isinghood and Haiyan Zhu

³§´¡³§-2ÌýAn Introduction to Survival Analysis

 Xianwei Li Yanqi Gao and Micky Liu
SAS-3 A Journey into Causal Inference Jingyue Huang Tianai Liao and Ziyi He

³§´¡³§-4ÌýStructural Causal Models

 Shiyu He Anne Zheng and Andie Cao

Fall 2023
Project Mentor Mentees

´¡²Ñ-1ÌýSingle-Compartment Conductance-Based Models of Cortical Neurons 

 Maliha Ahmed Erica Han, Vinyga Kumararajah
AM-2 Introduction to Random Features in Machine Learning Esha Saha Felicity Li, Minqiu Liu, Yixuan Wu

°ä°¿-1ÌýThe Tutte Polynomial

 Josephine Reynes Bandana Bajaj, Zoe Zou

°ä°¿-2ÌýGraph Minors

 Sepehr Hajebi Xinyue Fan, Lyncy Li

°ä³§-1ÌýDeep learning for brain-computer interfaces

 Lena Podina Akira Yoshiyama

°ä³§-2ÌýIntroduction to Explanable AI

 Trang Bui Sanika Poojary, Jaimee Yeung

±Ê²Ñ-1ÌýDistributions of Arithmetic Functions

Sourabhashis Das

 Harshita Pahwa, Xinlei Xu

±Ê²Ñ-2ÌýIntroduction to Tropical Geometry

 Nicole Kitt Zhiqian Ding, Xinran Tian

³§´¡³§-1ÌýTransfer Learning from a Statistical Perspective

 Jie Jian Kun Zhu, Samantha Wallis, Xinran Zheng

³§´¡³§-2ÌýAn Introduction to Causal Inference

 Jingyue Huang Christina Feng, Gengyang Chen, Sherry Chang

Spring 2023
Project Mentor Mentees
CO-1 The Hat Guessing Number of Graphs Jeremy Chizewer Shriya Kaistha and Mehrdad Sohrabi
°ä°¿-2ÌýModel-Based Derivative-Free Optimization Matthew Hough Jessica Ding and Hong Guan
CS-1 Bayesian Methods in Machine Learning Yueheng Zhang Alian Umali and Helena Xu
CS-2 Mathematics behind Machine Learning Shruti Srivatsan Tracy Hua and Bansari Shah
PM-1 Symmetries of the Rubik's Cube Sean Monahan Frank Zhu and Jingwen Shi
PM-2 Distribution of Prime Numbers Ismael El Yasini Sarah Cobean
SAS-1 Basic Asymptotic Statistics Trang Bui Sagun Malwatkar
SAS-2 Causal Inference: Mimicking Potential Outcomes on a Single Individual Henan Xu Jia Sheng Hu and Gioia de Leonardis
SAS-3 An Introduction to Bayesian Inference and Applications ³Û¾±°ù²¹²ÔÌý°Â²¹²Ô²µ Maisha Thasin and Vani Singh
SAS-4 An Introduction to Causal Inference Jingyue Huang Zhuofan Tang and Sana Thind
SAS-5 Random Walk and Percolation Models Tingzhou Yu Alicia Bremer

Winter 2023
Project Mentor Mentees
AM-1 Consensus seeking in multi-agent systems in both continuous time and discrete time protocols Hassan Qazi Xinyue Fan
AM-2 Neural network-based stability analysis for dynamical systems Ruikun Zhou Zaheer Mohideen

AM-3 Manifold Garden: A Story of Black Holes, Mathematical Theory behind Black Hole Physics

 Elly Moghtaderi Sri Krithika Venkatesh

CO-1 Graph Minors

 Mathieu Rundstrom Wendy Yang and Sneha Elavarasan
CO-2 Incidence Structures, Graphs, and Designs Sabrina Lato Vaani Rajpal
PM-1 Representation theory of algebras and applications Aiden Suter Sissy He and Samantha Pater
SAS-1 An investigation on the spatial autoregressive model Trang Bui Jaimee Yeung
SAS-2 An Introduction to Risk Optimization in Insurance Zhanyi Jiao Xinyu Wu
SAS-3 Arrow-Debreu Equilibria in Competitive Markets Michael Zhu Alicia Byron

Fall 2022
Project Mentor Mentees
CO-1 Graph Limits Lise Turner Mabel Kwok, Ying Shu
CO-2 Theory of Excluding Induced Subgraphs & The Erdős–Hajnal conjecture Aristotelis Chanioties Grace Sung
CO-3 Strongly Regular Graphs Sabrina Lato Erica Han, Laura Cao
AM-1 Ordinary Differential Equations in Mathematical Biology Nat Kendal-Freedman Maisha Thasin, Aadila Ali Sabry
PM-1 Mathematics of quantum field theory Aiden Suter Lily Mueller
PM-2 The Riemann-Roch Theorem for Curves Brady Ali Medina Remington Zhi
PM-3 Introduction to Non-Formking in Stable Theories Christine Eagles Lejing Li

Spring 2022
Project Mentor Mentees
AM-1 Mathematical modelling for women’s health ²Ñ±ð±ô¾±²õ²õ²¹Ìý³§³Ù²¹»å³Ù Chloe Li and Chang Liu
AM-2 On the role of the energy loss function in the image force on a charge moving over supported graphene María Rosa Preciado Rivas Siming Xu
CO-1 Chi-Boundedness: What is and isn't known about high chromatic numbers? ´¡±ô±¹²¹°ù´ÇÌý°ä²¹°ù²ú´Ç²Ô±ð°ù´Ç ·¡±ô¾±³ú²¹²ú±ð³Ù³óÌý³Û²¹³¦°ì´Ç²ú´Ç²õ°ì¾±
CO-2 Kolmogorov complexity Noah Weninger Jiawen Zhu
PM-1 Diophantine approximation & geometry of numbers ´³Ã©°ùé³¾²âÌý°ä³ó²¹³¾±è²¹²µ²Ô±ð ´³´Ç±ô¾±²Ô±ðÌý°ä³ó±ð²Ô²µ
PM-2 Positive Matrices ³¢²¹°ù¾±²õ²õ²¹Ìý°­°ù´Ç±ð±ô±ô Yiyang Huang and Wendy Lu

PM-3 Mermin-Peres Magic Square Game

Magic Square Game by Jennifer Zhu (PDF)

 ´³±ð²Ô²Ô¾±´Ú±ð°ùÌý´Ü³ó³Ü

Weixu Chen and Armaan Hussain
SAS-1 Learning from Data Using the Gaussian Process ²Ñ±ð¾±³æ¾±Ìý°ä³ó±ð²Ô ´¡±ô¾±³¦¾±²¹Ìý²Ñ²¹³Ù³ó±ð·É

See the list of similar programs at other institutions .