Current projects:
Past projects:
Spring 2023:
| Student |
Mentor |
Project topic |
Presentation title |
| Mari Sanders | Jason Brown | Using Networks to Model Disease Spread | |
| Yucong Chen | Jacob Swenberg | Category Theory | |
| Tom Hong | Rohan Joshi | Differential Geometry | |
| Sahngyoon Rhee | Rohan Joshi | Manifolds | |
| Aiqi You | Rohan Joshi | Fundamental Groups | |
| Elio Merolle | Jason Brown | Dimensionality Reduction | |
| Justin Pascua | Cecelia Higgins | Independence Results | |
| Xiaoxian Chen | Zachary Smith | Introduction to Julia Sets | |
| Surya Subbarao & Terry Wang & Menghan Wang | Josh Enwright & Colin Ni | Dynkin Diagrams and Lie Algebras |
Winter 2023:
| Student |
Mentor |
Project topic |
Presentation title |
| Tom Hong | Rohan Joshi | Differential Geometry | |
| Ruibin Lyu | James Chapman | Reinforcement Learning | |
| Jiayue Liu & George Luan | Alexander Tenenbaum | Random Graphs and the 0-1 Law in Logic | |
| Aidan Byer | Louis Esser | Algebraic Geometry/Schemes | |
| Terry Wang | Colin Ni | Elliptic Curve Arithmetic and the Mordell-Weil Theorem | |
| Aiqi You | Rohan Joshi | Cantor-Lesbesgue Function | |
| Lucas Duckworth | Zachary Smith | Hamel Bases in Banach Spaces | |
| Michael Pung | Bar Roytman | Fundamental Group | |
| Yucong Chen | Jacob Swenberg | Primes of the Form x^2+ny^2 |
Fall 2022:
| Student |
Mentor |
Project topic |
Presentation title |
| Justin Purnomo | Jack Luong | Approximation Theory | |
| Aiqi You | Rohan Joshi | Filters | |
| Max Steinberg | Ben Szczesny | Stable Homotopy | |
| Tom Hong | Rohan Joshi | Covering Spaces | |
| Justin Pascua | Cecelia Higgins | Ordinals and Cardinals | |
| Michael Pung | Bar Roytman | Algebraic Curves and the Nullstellensatz | |
| Jordyn Fuchs | Erin George | Support Vector Machines | |
| Frank Zheng | Colin Ni | Cobordism |
Spring 2022:
| Student |
Mentor |
Project topic |
Presentation title |
| Michael Pung | Bar Roytman | Galois Theory | |
| Justin Purnomo | Joyce Chew | Matrix Factorization | |
| Nilay Patel | Timothy Smits | Quadratic Reciprocity | |
| Zayan Shariff | Category Theory | ||
| Lekun Wang | Thierry Laurens | Real Analysis | |
| Zelong Li | Yan Tao | Knot Theory | |
| Liangjiawa Yuan | Rushil Raghavan | Probability | |
| Hunter Liu | Ben Spitz | Algebraic Geometry | |
| Brian Miyatake | Timothy Smits | Number Theory | |
| Jonathan Chang & Wenxin Xu | Nicholas Boschert | Fourier Transform |
Winter 2022:
| Student |
Mentor |
Project topic |
Presentation title |
| Angela East | Yan Tao | Knot Theory | |
| Corbin Balitactac | James Leng | Partial Differential Equations | |
| Isaac Li | David Soukup | Permutation Classes | |
| Glenn Sun | Colin Ni | Computational Algebraic Geometry | |
| Tom Hong | Rohan Joshi | Classification of Surfaces | |
| Hailey Weingord | Joe Breen | Lie Algebras and Lie Groups | |
| Isabelle Hong & Francis Park & Garrett Francisco | Harris Khan | Spectral Graph Theory | |
| Zheng Tan | Thierry Laurens | Functional Analysis | |
| Jiantong Liu | Ben Spitz | Enriched Categories |
Fall 2021:
| Student |
Mentor |
Project topic |
Presentation title |
| Max Steinberg | Riley Thornton | ||
| Logan Hyslop | Clark Lyons | forcing and weak forms of the axiom of choice | |
| Heqing Yin | Frederick Vu | Elliptic Curve Cryptography | |
| Jason Huang | Frederick Vu | Abel-Runffini Theorem | |
| Eric Wu | Alex Leng | Group Theory/Basic Algebra | |
| John Xiaoshu Zhou | Alex Leng | Representation Theory of Finite Groups | |
| Aric Cutuli | Xia Li | ||
| Isaac Li | David Soukup | permutation patterns | |
| Sasha Kononova | David Soukup | linear algebra techniques in combinatorics | |
| Haoyu Li | Nicholas Boschert | ||
| Wing Pok Lee | Nicholas Boschert | ||
| Zhenye Yang | Joe Breen | De Rham cohomology | |
| Xi Wu | Joe Breen | Bayesian statistics | |
| Samantha Alejandre | Joe Breen | gradient descent algorithm | |
| Xiaohe Zhang | Jerry Luo | Opinion Dynamics on Networks | |
| Chenxin Shen | Jerry Luo | Applied Topology and Topological Data Analysis | |
| Kyle Onghai | Colin Ni | Dirichlet's theorem on AP | |
| Wenlong Tang | Rushil Raghavan | Fourier Analysis | |
| Srinjana Sriram | Louis Esser | Introduction to algebraic topology. | |
| Xinyue Li | Joyce Chew | Convex Optimization Theory | |
| Ethan Warren | David Popovic | Introduction to Topology. | |
| Kevin Wong | Stan Palasek | nonconservative weak solutions for the euler equantions | |
| James Chen | Stan Palasek | computational schemes for mean field games. | |
| Nicola Sassone | Benjamin Bowman | ||
| Chenfei Li | Kyung Ha | ||
| Sahire Ellahy | Kyung Ha | ||
| Samantha Lee | Raymond Chu | ||
| Hongyi Yang | Ben Szczesny | "Applied category theory" |
Spring 2021:
| Student |
Mentor |
Project topic |
Presentation title |
| Ivan Tran | Ben Jarman | ||
| Jesse Chien | Ben Spitz | Homological algebra/derived functors | |
| Runze Yu | Ben Spitz | Finite groups | |
| Matthew Mallory | Ben Szczesny | ||
| Shangzie (Richard) Zhang | Christian Carrick | ||
| Henry Ma | Clark Lyons | ||
| Tanishq Bhatia | Jerry Luo | Topics in Persistent Homology | |
| Romina Deville | Kyung Ha | Understanding Chaos | |
| Yang Zhou | Louis Esser | Abelian varieties | |
| Charles Sowerby | Nicholas Boschert | ||
| Christine Tseng | Nicholas Boschert | ||
| Jingxuan Zhang | Raymond Chu | ||
| Rebecca Guo | Riley Thornton | Lectures on Network Systems by Bullo | |
| Angela Chen | Riley Thornton | Lectures on Network Systems by Bullo | |
| Alexander Lin | Wonjun Lee | Generative Adversarial Network (GAN). |
Winter 2021:
| Student |
Mentor |
Project topic |
Presentation title |
| Corbin Balitactac | Gyu Eun Lee | Asymptotic analysis | Asymptotic Integral Methods |
| Daniel Becerra | Kyung Ha | Dynamical systems & chaos | |
| Tanishq Bhatia | Jerry Luo | Persistent homology | |
| Angela Chen | Riley Thornton | Algebraic and spectral graph theory | Algebraic and spectral graph theory |
| Marc Andrew Choi | Kyung Ha | Spectral theory | |
| Anna Cusenza | Bjoern Bringmann | Partial differential equations | PDE's |
| Justine French | Alex Wertheim | Algebraic geometry | |
| Young He | Ben Spitz | ||
| Navin Khoshnan | Bar Roytman | ||
| William Lennox | Ben Szczesny | Algebraic Topology | Algebraic Topology |
| Alexander Lin | Wonjun Lee | Neural Networks | Neural Networks |
| Matthew Mallory | James Leng | Ergodic Theory | Ergodic Theory |
| Dan Rosen | Nicholas Boschert | ||
| Christine Tseng | Nicholas Boschert | Simple Random Walk on R | Simple Random Walk on R |
| Runze Yu | Ben Spitz | ||
| Shangjie Zhang | Christian Carrick | Stable homotopy theory | |
| Yang Zhou | Louis Esser | Toric varieties | |
| Hongyu Zhu | Bar Roytman |
Fall 2020:
| Student |
Mentor |
Project topic |
Presentation title |
| Corbin Balitactac | Bjoern Bringmann | Fourier Series and Equidistribution | |
| Louis Chaves Meyles | Laurent Vera | Quiver representations | Quiver Representations |
| Nuo Chen | Aaron Anderson | Algebraic combinatorics | |
| Emma Fisher | Aaron George | Topology | |
| Young He | Ben Spitz | Universal algebra | Universal Algebra |
| Rachmiel Klein | Eilon Tzur | Algebraic theory of numbers | |
| Sasha Kononova | Bar Roytman | ||
| Yik Li | Austin Christian | Knots and dynamics | |
| Charles Sowerby | Nicholas Boschert | ||
| Kartik Tandon | Bar Roytman | ||
| Runze Yu | Ben Spitz | Universal algebra | Universal Algebra |
| Yang Zhou | Louis Esser | Geometric invariant theory |
Spring 2020:
Note: The Spring 2020 DRP was cancelled due to the COVID-19 pandemic.
Winter 2020:
| Student |
Mentor |
Project topic |
(Colloquium cancelled due to COVID-19) |
| Meijke Balay-Mickelson | Blaine Talbut | ||
| Siqi Huang | Yudong Qiu | Algebraic number theory | |
| Ying Kit Hui | Laurent Vera | Morita theory | |
| Dylan Jamner | Eilon Tzur | ||
| William Legg | Austin Christian | Symplectic geometry/dynamics | |
| Walker Rice | Eilon Tzur | ||
| Anna Svirschevsky | Bar Roytman | ||
| Kartik Tandon | Bar Roytman | ||
| Xinta Yang | Gyu Eun Lee | Fourier analysis and wavelets | |
| Guoran Ye | Nicholas Boschert | ||
| Annie Zhang | Riley Thornton | ||
| Yang Zhou | Louis Esser | Quasicoherent sheaves, toric varieties, singularities | |
| Yi Zhou | Alex Wertheim | Algebraic geometry |
Fall 2019:
| Student |
Mentor |
Project topic |
Presentation title |
| Kyle Coughlin | Matthew McMillan | Categories via graphs and sets | Containment and Inclusion in Category Theory |
| Gabriel Fanucchi | Nicholas Boschert | ||
| Samanda Hu | Bar Roytman | Calculation of Group Homology | |
| Melissa Lee | Blaine Talbut | Partial differential equations | |
| William Legg | Austin Christian | Enumerative geometry | Enumerative Geometry of Lines on CPn |
| Walker Rice | Eilon Tzur | Algebraic topology | |
| Kartik Tandon | Bar Roytman | Group Homology through Simplicial Sets | |
| Xinta Yang | Gyu Eun Lee | Calculus of variations | Topics on Calculus of Variations |
| Yang Zhou | Louis Esser | Scheme theory | |
| Yi Zhou | Alex Wertheim | Algebraic geometry |
Spring 2019:
| Student |
Mentor |
Project topic |
Presentation title |
| James Atlas | Riley Thornton | Arithmetic hierarchy and randomness | |
| Meijke Balay-Mickelson | Eden Prywes | Quasiconformal maps | |
| Yunliang Chen | Bjoern Bringmann | ||
| Josef Cutler | Nicholas Boschert | Fundamentals of Riemannian geometry | |
| Joshua Enwright | Bjoern Bringmann | ||
| Yiheng He | Sang Truong | Riemann-Roch theorem | |
| Saamarth Juneja | Clark Lyons | ||
| Rachmiel Klein | Clark Lyons | ||
| Zhengjun Liang | Bar Roytman | ||
| Nicholas Liskij | Gyu Eun Lee | Asymptotic analysis of integrals | |
| Tyler Lopez | Austin Christian | Legendrian contact homology | |
| Aditya Nambiar | Joe Breen | Riemann mapping theorem, uniformization theorem | |
| Tachin Ruankriengsin | Adam Lott | Spectral graph theory | Spectral Graph Theory |
| Jas Singh | Kevin Carlson | ||
| Yan Tao | Will Baker | Algebraic topology | An application of fundamental groups |
| Eric Wang | Dohyun Kwon | Sets of finite perimeter and geometric variational problems | |
| Ryan Watson | Nicholas Boschert | Morse theory and classification of surfaces | Creating Manifolds with Morse Theory |
| Sian Wen | Riley Thornton | Fundamental groups and covering spaces | |
| Ken Willyard | Bon-Soon Lin | ||
| Richard Zhang | Robert Housden | ||
| Jason Zhao | Assaf Shani | ||
| Shend Zhjeqi | Bjoern Bringmann |
Winter 2019:
| Student |
Mentor |
Project topic |
Presentation title |
| Anish Chedalavada | Ian Coley | Bott periodicity & topological K-theory | Topological K-Theory |
| Raymond Chu | Blaine Talbut | Optimal transport | Optimal Transportation |
| Ethan Davis | Louis Esser | Category theory | Quantifiers as Adjoints |
| Dyusha Gritsevskiy | Frederick Vu | Finite dimensional representations of semisimple Lie algebras over C | Lie Groups in Physics |
| Bryan Hu | Alex Dobner | Number theory | |
| Samanda Hu | Bar Roytman | Algebraic number theory | Splitting of Prime Ideals in Quadratic Field Extensions |
| Saamarth Juneja | Clark Lyons | ||
| Unchitta Kanjanasaratool | Denali Molitor | Interpretability of machine learning methods | |
| Rachmiel Klein | Clark Lyons | The Cycle Space and Simplicial Complexes | |
| William Legg | Alex Mennen | First-order logic | Gödel's Completeness Theorem and applications |
| Zhengjun Liang | Bar Roytman | Algebraic topology | Applications of Algebraic Topology on Graphs |
| Nicholas Liskij | Gyu Eun Lee | Functional analysis & distribution theory | Functional Analysis and Distributions |
| Tyler Lopez | Austin Christian | Legendrian knots | Legendrian Knots |
| Jackson Morris | Abigail Hickok | ||
| Jiarui Qu | Kevin Carlson | Category theory | |
| Vincent Robbins | Thomas Gilton | Descriptive set theory | Axiom of Determinacy & PSP in Polish Spaces |
| Jas Singh | Kevin Carlson | Higher category theory | |
| Eric Wang | Dohyun Kwon | Sets of finite perimeter and geometric variational problems | An isoperimetric inequality |
| Yang Wang | Eden Prywes | ||
| Sian Wen | Riley Thornton | ||
| Ruofei Wu | Chris Shriver | Markov chains and mixing times | |
| Guoran Ye | Bar Roytman | Algebraic topology | Applications of Algebraic Topology on Free Groups |
| Richard Zhang | Robert Housden | Higher homotopy group |
Fall 2018:
| Student |
Mentor |
Project topic |
Presentation title |
| Urte Adomaityte | Frederick Vu | Topology, Nielsen-Schreier theorem | |
| Joshua Enwright | Mike Miller | Differential topology | Differential Topology |
| Bryan Hu | Blaine Talbut | Harmonic analysis on locally compact abelian groups | Fourier Transform on LCA Groups |
| Samanda Hu | Bar Roytman | Algebraic number theory | Algebraic Integers in Quadratic Fields |
| Saamarth Juneja | Clark Lyons | Infinitary Combinatorics | |
| Unchitta Kanjanasaratool | Denali Molitor | Interpretability in basic machine learning methods | Sparse Linear Models and Interpretability |
| Rachmiel Klein | Clark Lyons | Knot theory: Reidemeister and invariants | |
| Tyler Lopez | Austin Christian | Morse theory | Morse Theory |
| Aditya Mallick | Mike Miller | Differential forms and homological algebra | Sheaves and equivalent cohomology theories |
| Jackson Morris | Abigail Hickok | Morse Theory | |
| Daniel Ragsdale | Bar Roytman | Differential topology | The Jordan-Brouwer separation theorem |
| Sam Rhee | Gyu Eun Lee | Maximal function theory | |
| Vincent Robbins | Thomas Gilton | Descriptive set theory | The Borel Hierarchy |
| Krysten Schmidt | Will Oakley | ||
| Nirmay Singaram | Riley Thornton | Galois theory via model theory | Model Theoretic Approach to Galois Theory |
| Jas Singh | Kevin Carlson | A Categorical Approach to Universal Algebra | |
| Yang Wang | Eden Prywes | Stochastic differential equations | Ito Calculus |
| Sian Wen | Riley Thornton | Model theory | Quantifier Elimination |
| Ken Willyard | Bon-Soon Lin | Spanning trees in complete bipartite graphs | |
| Richard Zhang | Robert Housden | Brief intro to homology functor | |
| Michael Zshornack | David Hemminger | Algebraic topology | The Brouwer fixed point theorem via homotopy |
Summer 2018:
| Student |
Mentor |
Project topic |
Presentation title |
| William Black | Gyu Eun Lee | Fourier analysis | |
| Juan Carbajal | Riley Thornton | Graph theory & algebraic combinatorics | Stationary Distribution |
| Manuel Chavez | Blaine Talbut | Ordinary differential equations | Geometric look at ODEs |
| Collin Cranston | David Jekel | Free probability & random matrices | Free Probability and Free Independence |
| Joshua Enwright | Kevin Carlson | Classification of compact surfaces | Classification of compact surfaces |
| Rong Fan | Austin Christian | Low dimensional geometry | Farey Tessellations |
| Yuan Fang | Alex Frederick | ||
| Kiyotaka Hachisuka | Eli Sadovnik | PDE & finite element method | Finite Element Method |
| Yujie He | Michelle Feng | Fundamental Theorem of Asset Pricing | |
| Arin Khudaverdyan | David Jekel | Probability & measure theory | |
| Karina Sanchez | Thomas Gilton | Introduction to mathematical logic | Topics of Mathematical Logic |
| Iris Sun | Riley Thornton | Model theory | 0-1 Law for Random Graphs |
| Yang Wang | Gyu Eun Lee | Partial differential equations | |
| Michael Zshornack | David Hemminger | Representation theory of finite groups | Representation Theory of Groups and Its Uses |