# 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.