Research

I am interested in algebraic topology, (abstract) homotopy theory, and (higher) category theory.

My PhD project approaches rational homotopy theory in the framework of model categories and simplicial sets, and it establishes connections of this approach with the study of categories up to homotopy, that is, (∞, 1)-categories.

My PhD thesis is on models for rational (∞, 1)-categories. I introduce rational (∞, 1)-categories, which are (∞, 1)-categories enriched in spaces whose higher homotopy groups are rational vector spaces, and I provide equivalent models for rational (∞, 1)-categories. Two such models are

1. rational complete Segal spaces, which are based on Rezk's complete Segal space model for (∞, 1)-categories; and

2. rational Segal categories, which are based on Bergner's models for (∞, 1)-categories using Segal categories.

Although my models hinge on my work on the rational homotopy theory of non-simply connected spaces using the toolkit of model categories, my methods work for (∞, 1)-categories enriched in general localizations of spaces.

Preprints

Models for rational (∞, 1)-categories, preprint available at arXiv:2509.22413 [math.AT].

A modern perspective on rational homotopy theory, preprint available at arXiv:2505.23322 [math.AT].

Talks

"Models for rational (∞, 1)-categories", JMM Special Session on New Voices in Homotopy Theory, January 2026 (planned)

"Models for rational (∞, 1)-categories", 2025 Category Theory Octoberfest, virtual talk with online recording, October 2025 (slides)

"Models for rational (∞, 1)-categories", University of Kentucky Topology Seminar, October 2025

"A modern perspective on rational homotopy theory", University of Virginia Graduate Seminar, October 2025

"Rational complete Segal spaces", Transactions in Category Theory, virtual talk, June 2025

"Rational complete Segal spaces", GTA Philadelphia, Temple University, June 2025

"The rational model structure on reduced simplicial sets", Upstate New York Topology Seminar (UNYTS), Binghamton University, March 2025

"The rational model structure on reduced simplicial sets", University of Virginia Topology Seminar, February 2025

"Simplicial methods in rational homotopy theory", University of Virginia Graduate Seminar, November 2024

"An introduction to rational homotopy theory", University of Virginia Graduate Seminar, September 2023

"An introduction to rational homotopy theory", Graduates Reminisce Online On Topology (GROOT) Summer Seminar, virtual talk available on YouTube, June 2023