Research

Current Research

I’m generally interested in problems related to topology, algebra and combinatorics. It’s always great fun when I can use my computer science background to help me tackle pure math problems. Lately, I’ve been thinking about applications of topological data analysis to cancer genomics and Eastwood-Huggett-style categorification. As part of a group from REACT, I’m also thinking about Ehrhart theory and order polytopes. In my spare time I sometimes study problems related to Fibonacci numbers, Turner’s retract theorem and Conway’s Game of Life on a random graph. In the past I’ve worked on problems related to knot theory, graph theory and inscribability problems (through the lens of topological combinatorics).

Past Research

During the summer of 2017 I attended an REU at Cornell University under the advisorship of Dr. Florian Frick. While there I worked on two problems. The first was determining the chromatic number of a specific family of hypergraphs. The second was about splitting closed loops which is closely related to the square peg problem. While at Northeastern University I completed an undergraduate thesis where I considered the following question. What happens when one discretizes a knot and changes the order the vertices are connected in?

Publications

Splitting Loops and Necklaces: Variants of the Square Peg Problem with Shujian Chen, Florian Frick, Sam Saloff-Coste, Linus Setiabrata and Hugh Thomas – Forum Math., Sigma, 8, e5 (2020). arXiv version

On the generalized Erdős–Kneser conjecture: proofs and reductions with Shuli Chen, Ethan Coldren, Florian Frick and Linus Setiabrata – J. Combin. Theory, Ser. B, 135 (2019): 227-237. arXiv version

Classes

I am currently (Spring 2021) taking: Combinatorics of Coxeter Groups, Algebraic Topology II at Duke (Auditing), Minicourse on Knot Homology Theories and doing research.

I have passed qualifying exams in Topology, Algebra and Combinatorics.

Fall 2020: Intro to Machine Learning in Biology, Reading Course: Categorification, Reading Course: Topological Data Analysis.

Spring 2020: Nonlinear Programming, Schubert Calculus, Reading Course: Categorification.

Fall 2019: Algebraic Topology II, Topological Combinatorics, Reading Course: Categorification.

Spring 2019: Algebra II, Combinatorics II, Riemannian Geometry, Algebraic Topology.

Fall 2018: Algebra I, Combinatorics I and Manifold Theory.

Undergraduate Thesis

“The Action of the Symmetric Group on a Tame Knot” – Advisor: Dr. Ivan Martino Committee: Dr. Ivan Martino, Professor David Massey and Professor Anthony Iarrobino.