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).
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?
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
I am currently (Fall 2021) taking: Topics in Topology and doing research.
I have passed qualifying exams in Topology, Algebra and Combinatorics.
Spring 2021: Combinatorics of Coxeter Groups, Algebraic Topology II at Duke (Auditing), Minicourse on Knot Homology Theories.
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.
“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.