Research
My research focuses on connections between topology, algebra, higher category theory, and physics; I am especially interested in the interplay between Heegaard Floer homology and higher representation theory.
In preparation
From hypertoric geometry to bordered Floer homology via the m=1 amplituhedron II, joint with A. D. Lauda and A. M. Licata
Toward the Heegaard Floer homology of a point
Preprints
Evaluations of link polynomials and recent constructions in Heegaard Floer theory, joint with L. Gu
Trivalent vertices and bordered knot Floer homology in the standard basis
Higher representations and cornered Heegaard Floer homology, joint with R. Rouquier
From hypertoric geometry to bordered Floer homology via the m=1 amplituhedron, joint with A. D. Lauda and A. M. Licata
Published works
Ozsváth-Szabó bordered algebras and subquotients of category O, joint with A. D. Lauda, published in Advances in Mathematics
Singular crossings and Ozsváth-Szabó's Kauffman-states functor, published in Fundamenta Mathematicae
Strands algebras and Ozsváth-Szabó's Kauffman-states functor, joint with M. Marengon and M. Willis, published in Algebraic & Geometric Topology
Generators, relations, and homology for Ozsváth-Szabó's Kauffman-states algebras, joint with M. Marengon and M. Willis, published in Nagoya Mathematical Journal
On two types of Heegaard diagram used in knot Floer homology, published in Michigan Mathematical Journal
On the decategorification of Ozsváth and Szabó's bordered theory for knot Floer homology, published in Quantum Topology
The Khovanov homology of 3-strand pretzels, revisited, published in New York Journal of Mathematics
Khovanov-Seidel quiver algebras and Ozsváth-Szabó's bordered theory; published in Journal of Algebra
On bordered theories for Khovanov homology; published in Algebraic & Geometric Topology
The rational Khovanov homology of 3-strand pretzel links; published in Journal of Knot Theory and its Ramifications
A sign assignment in totally twisted Khovanov homology; published in Algebraic & Geometric Topology
The critical group of a line graph, joint with A. Berget, M. Maxwell, A. Potechin, and V. Reiner; published in Annals of Combinatorics
Other works
Constructions and computations in Khovanov homology (Ph.D. thesis, Princeton)
Heegaard Floer homology and knots (expository paper written for Part III at Cambridge)
Two approaches to the embedding of Riemann surfaces in projective space (undergraduate thesis at Notre Dame)
The virtually cyclic classifying space of the Heisenberg group, joint with L. Pham and J. Poelhuis (REU project at Notre Dame)