Past DRP Projects

Fall 2024 mentors and their projects

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
AM-1 Numerical 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
AM-3 Efficient 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
CO-1 Helly's theorem in the plane and beyond? Mathieu Rundstrom Heer Mehta and Sneha Elavarasan
CO-2 Tyshkevich 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
CS-1 MathCraft: The Tower of Hanoi Odyssey Punit Kunjam Sophia Zhu, Luna Wu, and Alia Cai
CS-2 Evaluating 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
CS-5 The 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 | Ananya's GitHub repository

 Spencer Szabados Ananya Kumar and Zayaan Mulla
PM-1 Wallpaper Groups AJ Fong Bethelhem Bezabeh and Melody Tian
PM-2 Introduction to Elliptic Curves and Modular Forms Yash Totani Bryan Chen and Natalia Weber
PM-3 Structure 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
SAS-1 Causal Inference: Mimicking Potential Outcomes on a Single Individual Henan Xu Xinyang Li, Tiffany Wang, and Zhige Chen
SAS-2 What 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

SAS-4 Deciphering 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

SAS-6 Introduction to Missing Data Problem in Health Data

 Yuliang Shi Shuha Sheikh

Winter 2024

Winter 2024 DRP Projects

Project Mentor Mentees
AM-1 Mathematical 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

AM-3 Dynamics of the Neural Network

 Liang Chen Natalia Manturowicz and Alicia Lin

CO-1 Robust 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

CS-1 Introduction 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
CS-5 Algorithms 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
CS-7 The Graph Container Method and Applications in Algorithms Cameron Seth Aadila Ali Sabry
PM-1 Introduction 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

PM-3 Why does the golden ratio show-up in flowers?

 Jérémy Champagne Jackie Liu and Lydia He

SAS-1 Introduction to Bayesian Inference

 Yiran Wang Keeley Isinghood and Haiyan Zhu

SAS-2 An 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

SAS-4 Structural Causal Models

 Shiyu He Anne Zheng and Andie Cao

Fall 2023
Project Mentor Mentees

AM-1 Single-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

CO-1 The Tutte Polynomial

 Josephine Reynes Bandana Bajaj, Zoe Zou

CO-2 Graph Minors

 Sepehr Hajebi Xinyue Fan, Lyncy Li

CS-1 Deep learning for brain-computer interfaces

 Lena Podina Akira Yoshiyama

CS-2 Introduction to Explanable AI

 Trang Bui Sanika Poojary, Jaimee Yeung

PM-1 Distributions of Arithmetic Functions

Sourabhashis Das

 Harshita Pahwa, Xinlei Xu

PM-2 Introduction to Tropical Geometry

 Nicole Kitt Zhiqian Ding, Xinran Tian

SAS-1 Transfer Learning from a Statistical Perspective

 Jie Jian Kun Zhu, Samantha Wallis, Xinran Zheng

SAS-2 An 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
CO-2 Model-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 Yiran Wang 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

Sri Krithika's Presentation.pdf

 Elly Moghtaderi Sri Krithika Venkatesh

CO-1 Graph Minors

Sneha and Wendy's DRP Presentation.pdf

 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 Melissa Stadt 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? Alvaro Carbonero Elizabeth Yackoboski
CO-2 Kolmogorov complexity Noah Weninger Jiawen Zhu
PM-1 Diophantine approximation & geometry of numbers Jérémy Champagne Joline Cheng
PM-2 Positive Matrices Larissa Kroell Yiyang Huang and Wendy Lu

PM-3 Mermin-Peres Magic Square Game

Magic Square Game by Jennifer Zhu (PDF)

 Jennifer Zhu

Weixu Chen and Armaan Hussain
SAS-1 Learning from Data Using the Gaussian Process Meixi Chen Alicia Mathew

See the list of similar programs at other institutions here.