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.
Toward the Heegaard Floer homology of a point, joint with R. Arian
A symmetric monoidal Frohman-Nicas TQFT for sutured manifolds, joint with E. Rutter
A-infinity categories, A-infinity functors, and pre-natural transformations form an (A-infinity,2)-category, joint with C. Portwood
Trivalent vertices and bordered knot Floer homology in the standard basis; accepted for publication at Geometry & Topology (2020)
Higher representations and cornered Heegaard Floer homology, joint with R. Rouquier (2020)
Spectral 2-actions, foams, and frames in the spectrification of Khovanov arc algebras, joint with A. Dranowski, M. Guo, and A. D. Lauda; published in Transactions of the American Mathematical Society (2025)
On the decategorification of some higher actions in Heegaard Floer homology; published in Algebraic & Geometric Topology (2024)
From hypertoric geometry to bordered Floer homology via the m=1 amplituhedron, joint with A. D. Lauda and A. M. Licata, published in Selecta Mathematica (2024)
Surface gluings with signs and gradings in decategorified Heegaard Floer theory, published in International Mathematics Research Notices (2024)
Decategorified Heegaard Floer theory and actions of both E and F; published in Quantum Topology (2024, online first)
Compatibility in Ozsvath-Szabo's bordered HFK via higher representations, joint with W. Chang, published in Pacific Journal of Mathematics (2023)
Strands algebras and the affine highest weight property for equivariant hypertoric categories, joint with A. D. Lauda and A. M. Licata, published in Advances in Mathematics (2023)
Evaluations of link polynomials and recent constructions in Heegaard Floer theory, joint with L. Gu; published in Michigan Mathematical Journal (2023)
Generators, relations, and homology for Ozsváth-Szabó's Kauffman-states algebras, joint with M. Marengon and M. Willis, published in Nagoya Mathematical Journal (2021)
On two types of Heegaard diagram used in knot Floer homology, published in Michigan Mathematical Journal (2021)
Singular crossings and Ozsváth-Szabó's Kauffman-states functor, published in Fundamenta Mathematicae (2021)
Ozsváth-Szabó bordered algebras and subquotients of category O, joint with A. D. Lauda, published in Advances in Mathematics (2021)
Strands algebras and Ozsváth-Szabó's Kauffman-states functor, joint with M. Marengon and M. Willis, published in Algebraic & Geometric Topology (2020)
On the decategorification of Ozsváth and Szabó's bordered theory for knot Floer homology, published in Quantum Topology (2019)
The Khovanov homology of 3-strand pretzels, revisited, published in New York Journal of Mathematics (2018)
Khovanov-Seidel quiver algebras and Ozsváth-Szabó's bordered theory; published in Journal of Algebra (2017)
On bordered theories for Khovanov homology; published in Algebraic & Geometric Topology (2017)
The rational Khovanov homology of 3-strand pretzel links; published in Journal of Knot Theory and its Ramifications (2014)
A sign assignment in totally twisted Khovanov homology; published in Algebraic & Geometric Topology (2014)
The critical group of a line graph, joint with A. Berget, M. Maxwell, A. Potechin, and V. Reiner; published in Annals of Combinatorics (2012)
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)