Projects from Previous DRPs

Winter 2025

Selected for Math Club Session:  

• Not All Proofs Are Enough. Student: Sharif Velasquez. Mentor: Dhruv Kulshreshtha

• Hahn-Banach... Who's There? Student: Francisco Vigil. Mentor: Maria Madrugo

• Commutative Rings, Affine Schemes, and the Dictionary Between. Student: Gavin Lauer. Mentor: Riku Kurama

Abstracts and titles of all final presentations can be found here.

Fall 2024

Selected for Math Club Session:  

• Random forests. Student: Max Wang. Mentor: Sam Cochran

• Exploring Algebraic Methods in Differential Equations. Student: Saja Gherri. Mentor: Timothy Cheek

• Diophantine Systems and the Four Distance Problem. Student: Tyler Weeks. Mentor: Dhruv Kulshreshtha

Abstracts and titles of all final presentations can be found here.

Summer 2024

Selected for Math Club Session:  

• Dynamic Optimization and Real World Applications. Student: Tia Scarsella. Mentor: Sam Cochran

• Rotations and Orthogonal Representations with Applications in Robotics. Student: Julian Skifstad. Mentor: Dhruv Kulshreshtha

• Breaking Down Elliptic Curve Cryptography. Student: Harish Jaisankar. Mentor: Zander Hill

Abstracts and titles of all final presentations can be found here.

Winter 2024

Selected for Math Club Session:  

• Exploring Patterns in Complex Dynamics – From Simple Doublings to Intricate Multibrots. Student: Tia Scarsella. Mentor: Katia Shchetka

• Stochastically Modeling Chemical Reactions. Student: Mitchell Godek. Mentor: Shivani Prabala

• Representations of sl(2, C). Student: Albon Wu. Mentor: Sadie Lipman

Abstracts and titles of all final presentations can be found here.

Fall 2023

Selected for Math Club Session:  

• Survey of Financial Applications of Probability. Student: Carlos Rosales. Mentor: Marc Andrew Choi

• Infinity and the Banach-Tarski Paradox. Student: Raashi Ramanan. Mentor: Olivia Strahan

• An Introduction to Braid Groups. Student: Maxwell Natonson. Mentor: Runji Li

Abstracts and titles of all final presentations can be found here.

Winter 2023

Selected for Math Club Session:  

• An Introduction to the Algebra-Geometry Dictionary. Student: Rose Gerson. Mentor: Kaya Lakein

• Text Generation with Markov Chains and Recurrent Neural Network (RNN). Student: Eric Khiu. Mentor: Tejaswi Tripathi

• An Introduction to Discrete-Time Martingales. Student: Alankar Shende. Mentor: Sameer Kailasa

Abstracts and titles of all final presentations can be found here.

Fall 2022

Selected for Math Club Session:  

• Rational Points on Elliptic Curves. Student: Abigail Hess. Mentor: Kaya Lakein

• The Chip-Firing Game. Student: Jiaqi Lu. Mentor: Benjamin Baily

• Sketching Phase Portraits. Student: Daniel Cross. Mentor: Joe Huang

Abstracts and titles of all final presentations can be found here.

Winter 2022

Selected for Math Club Session:  

• Triangle Reflection Groups on the Hyperbolic Plane. Student: Josef Sajonz. Mentor: Bradley Zykoski

• Reflection Symmetries and Root Systems. Student: Pranjal Sharma. Mentor: Will Dana

Abstracts and titles of all final presentations can be found here.

Fall 2021

Selected for Math Club Session:  

• Applying Black Scholes to the Real World. Student: Vishal Nayak. Mentor: April Nellis.

• Proofs of the Isoperimetric Inequality. Student: Ashvin Pai. Mentor: Shelby Cox.

• The Projective Plane and Bezout's Theorem. Student: Yanjun Chen. Mentor: Gary Hu.

Final Presentations (Abstract Booklet):

• Applying Black Scholes to the Real World. Student: Vishal Nayak. Mentor: April Nellis.

• Proofs of the Isoperimetric Inequality. Student: Ashvin Pai. Mentor: Shelby Cox.

• Linear Programming and the Ellipsoid Method with Applications. Student: Wentao Xu. Mentor: Anthony Della Pella.

• The Projective Plane and Bezout's Theorem. Student: Yanjun Chen. Mentor: Gary Hu.

• Bezout's Theorem for Plane Curves. Student: Audy Lebovitz. Mentor: Carsten Sprunger.

• DeRham Cohomology and the Poincare Lemma. Student: Neville Joshua Rajappa. Mentor: Reebhu Bhattacharyya.

• Applications of the Crossing Number to Planar Geometry. Student: Henry Fleischmann. Mentor: Will Dana.

Winter 2021

Selected for Math Club Session:

• An Introduction to Markov Chains. Student: Karl Goddard. Mentor: Ryan Kohl.

• The Prime Number Theorem and the Riemann Zeta Function. Student: Neel Mougdal. Mentor: Patrick Kelley.

• The Stoke's Theorem that Calc III Doesn't Teach You. Student: Xuyan Liu. Mentor: Reebhu Bhattacharyya.

Final Presentations (Abstract Booklet):

• An Introduction to Markov Chains. Student: Karl Goddard. Mentor: Ryan Kohl.

• Random Walks. Student: Renjie Shao. Mentor: Yiwang Chen.

• The Prime Number Theorem and the Riemann Zeta Function. Student: Neel Mougdal. Mentor: Patrick Kelley.

• Prime Numbers and the Riemann Hypothesis. Student: Rajas Gupta. Mentor: Alex Horawa.

• Strategic Games and Nash Equilibria. Student: Yuhan Xiao. Mentor: April Nellis.

• Random Matrix Theory and Applications to Portfolio Optimization. Student: Rohit Chakravarty. Mentor: Andrew McMillan.

• Rational Points on Elliptic Curves. Student: Jeremy Flics. Mentor: Katja Vassilev.

• Hilbert's 10th Problem. Student: Syed Akbari. Mentor: Will Dana.

• The Stoke's Theorem that Calc III Doesn't Teach You. Student: Xuyan Liu. Mentor: Reebhu Bhattacharyya.

• Knot Invariants. Student: Xun Wang. Mentor: Christopher Zhang. 

• The Hartman-Grobman Theorem: Approximating Nonlinear Dynamical Systems. Student: Horacio Moreno Montanes. Mentor: Saibal De.

Fall 2020

Selected for Math Club Session:

• Data Analysis with Truncated SVD on the Eigenfaces. Student: Chang Wang. Mentor: Saibal De.

• Isometries of the Hyperbolic Plane. Student: Cassandra Prokopowicz. Mentor: Christopher Zhang.

• Mean-Field Games and their Social Applications. Student: Krista Hart. Mentor: April Nellis.

Final Presentations (Abstract Booklet):

• Two Limit Theorems. Student: Yiwei Fu. Mentor: Yili Zhang.

• Law Of Large Numbers. Student: Renjie Shao. Mentor: Yiwang Chen.

• Symmetries of Symmetric Groups. Student: Matthew Wang. Mentor: Ilia Nekrasov.

• Burnside’s Lemma: Using Group Theory to Count Distinct Objects. Student: Huixi Yao. Mentor: Oscar Gonzalez.

• Yoneda Lemma and Some Applications. Student: Yingzi Yang. Mentor: Yunze Lu.

• You Need a Lemma. Student: Faye Jackson. Mentor: Lukas Scheiwiller.

• Finite Difference Methods for Boundary Value Problems. Student: Haijian Wu. Mentor: John Wakefield.

• Data Analysis with Truncated SVD on the Eigenfaces. Student: Chang Wang. Mentor: Saibal De.

• Demystifying Groups: The Essence of Representation Theory. Student: Antareeksh Deb. Mentor: Carsten Sprunger.

• Isometries of the Hyperbolic Plane. Student: Cassandra Prokopowicz. Mentor: Christopher Zhang.

• Frobenius Elements in Galois Extensions. Student: Zheng Yang. Mentor: Kannappan Sampath.

• Random Walks on Electrical Networks. Student: Joshua Pickard. Mentor: Will Dana.

• Mean-Field Games and their Social Applications. Student: Krista Hart. Mentor: April Nellis.

Spring/Summer 2020

Final Presentations (Abstract Booklet):

• Trisecting an Angle. Student: Dianhui Ke. Mentor: Attilio Castano.

• Introduction to Representations on a Finite Group. Student: Bohan Xu. Mentor: Swaraj Sridhar Pande.

• The Coin-Exchange Problem of Frobenius. Student: Zachary Fewkes. Mentor: Rachel Webb.

• The Hasse-Minkowski Theorem - Rational Points of a Conic Section. Student: Zijian Rong. Mentor: David Schwein.

• The p-adic Numbers and their Applications for Finding Rational Solutions to Conic Equations. Student: Quinn Allchin. Mentor: Jason Liang.

• Mahler Expansions for p-adic Functions. Student: Seth Greenfield. Mentor: Eamon Quinlan-Gallego.

• Cauchy’s Theorem. Student: Chris Jiang. Mentor: Yueqiao Wu.

• Perspectives on Riemann Surfaces: Translating Analysis to Algebra. Student: Vikram Mathew. Mentor: Ruian Chen.

• Steiner Symmetrization and Geometric Inequalities. Student: Josh Messing. Mentor: Yonatan Shelah.

• What are Manifolds? Student: Wendy Wang. Mentor: Zhan Jiang.

• Introduction to Algebraic Geometry. Student: Ziyi Zhang. Mentor: Devlin Mallory.

• The Fundamental Group of a Circle. Student: Jonah Weinbaum. Mentor: Karthik Ganapathy.

• Introduction to Representation Theory of Finite Groups. Student: Lillian McPherson. Mentor: Kannappan Sampath.

• Representing Symmetries with Matrices. Student: Jonah Nan. Mentor: Michael Mueller.

• Smooth Manifolds and Lie Groups. Student: Joey Minnella. Mentor: Abigail Finlay.

• Compressed Sensing and Non-Parametric Regression. Student: Elizabeth Martin. Mentor: Christiana Mavroyiakoumou.

• Reducing Training Variances through Random Forest. Student: Lance Ying. Mentor: Saibal De.

Winter 2020

Note: The program was partially suspended on account of the COVID-19 pandemic.

Selected for Math Club Session (Abstract Booklet):

• The Point at Infinity: What is the Degree of 1/z? Student: Faye Jackson. Mentor: Christopher Zhang.

• Inequivalent Colorings and How to Count Them. Student: Zihong Yi. Mentor: David Schwein.

• Primes of the Form x² + ny². Student: Yuqing Liu. Mentor: Aleksander Horawa.

• Devil-Angel Game. Student: Xiaoqi Peng. Mentor: Will Dana.

Student Write-ups:

• Representation Theory and Maschke's Theorem. Student: Wen Plotnick. Mentor: Jack Carlisle. 

Fall 2019

Final Presentations (Abstract Booklet):

• Cheating Fate: Constructing Globally Defined Smooth Maps on Real Manifolds. Student: Christian Capanelli. Mentor: Daniel Irvine.

• Curvature, and How to Quantify It. Student: Arav Agarwal. Mentor: Carsten Peterson.

• The Teichmueller Space of the Torus. Student: Yichen (Jason) Liu. Mentor: Mark Greenfield.

• How Do Algebraic Curves Intersect?. Student: John (Jack) Haviland. Mentor: Aleksander Horawa.

• The Zariski Topology. Student: Bencheng Li. Mentor: Jason Liang.

• Representability of Group Functors. Student: Zhou Fang. Mentor: Kannappan Sampath.

• An Introduction to Mapping Class Groups. Student: Justin Vorhees. Mentor: Christopher Zhang.

• Topology of Surfaces. Student: Christopher Tait. Mentor: Jack Carlisle.

• How to Turn 3-Dimensional Space into e-Dimensional Space. Student: Josh Messing. Mentor: Ruian Chen.

• Introduction to Fourier Transformation and Applications in File Compression. Student: Adam DeHollander. Mentor: Ryan Kohl.

• Solving a Boundary Value Problem Using Fourier Series. Student: Trevor Gravely. Mentor: Joseph Kraisler.

• Solution Techniques for PDEs and Applications to Fluids. Student: Nasser Mohammed. Mentor: Christiana Mavroyiakoumou.

• Graph Embeddings and the Heawood Theorem. Student: Ethan Cohen. Mentor: William Dana.

• Central Limit Theorem for Length of Longest Increasing Subsequence. Student: Chen Shang. Mentor: Yuchen Liao.

• Arithmetic Functions and Dirichlet Convolution. Student: Andrew Nguyen. Mentor: Angus Chung.

• Primes of the Form p = x² + ny² and Euler’s "Convenient" Numbers. Student: Ethan Mook. Mentor: Andrew O’Desky.

• Disecting and Trisecting Angles. Student: Avi Tachna-Fram. Mentor: Zhan Jiang.

• An Accurate Representation of Linear Representation Theory. Student: Matthew Cunningham. Mentor: Hyung Kyu Jun.

• Knots and Knot Invariants. Student: Hannah Moon. Mentor: Farrah Yhee.

• Visualizing Complex Numbers and Functions. Student: Shuyang Zhang. Mentor: Michael Mueller.

• Elliptic Functions: Meromorphic Functions on the Torus. Student: Zijian Rong. Mentor: David Schwein.

• Uniform Convergence and Weierstrass Approximation Theorem. Student: Sai Zheng. Mentor: Sanal Shivaprasad.

Winter 2019

• Elliptic Curves and Cryptography. Student: Robert Larese. Mentor: Aleksander Horawa.

• Introduction to Probability. Student: Xueyi Zhu. Mentor: Karen Butt.

• Visualizing Complex Analysis. Student: Cyril Cordor. Mentor: David Schwein.

• Stability of the Predator-Prey System via Phase Portraits. Student: Ziyi Zhou. Mentor: Saibal De.

Fall 2018

• Primes of the form x² + ny². Student: Pleum Piriyatamwong. Mentor: David Schwein.

• Matrix Groups. Student: Noah McNeal. Mentor: Karen Butt.