My research is in algebraic topology, category theory and its connections with Ktheory and computer science. I explore stable homotopy theory, which involves algebraic structures on topological spaces. I investigate the coherence of these structures when defined up to homotopy. This leads to the concept of ∞loop spaces and their connection to spectra, representing homology and cohomology theories. I utilize model categories and ∞categories to study these structures. Additionally, I examine coalgebraic structures, their encoding of algebraic structures, and their applications in theoretical computer science. I also explore new trace methods to approximate algebraic Ktheory using variants of topological Hochschild homology.
My Research
Publications
6
Coinductive control of inductive data types, with Paige Randall North, to appear on 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)
5
SpanierWhitehead duality for topological coHochschild homology, with Haldun Özgür Bayındır, to appear in Journal of the London Mathematical Society
4
Koszul Duality in Higher Topoi, with Jonathan Beardsley, Homology, Homotopy and Applications 25 (2023), no. 1, 5370.
3
Coalgebras in the DwyerKan Localization of a Model Category, Proceedings of American Mathematical Society 150 (2022), no. 10, 4173–4190
2
The Coalgebraic Enrichment of Algebras in Higher Categories, Journal of Pure and Applied Algebra 226 (2022), no. 3.
1
Coalgebras in symmetric monoidal categories of spectra, with Brooke Shipley, Homology, Homotopy and Applications 21 (2019), no.1, 118.
0
Highly Structured Coalgebras and Comodules, PhD thesis (May 2020).
4
Preprints

Trace Methods for coHochschild homology, with Sarah Klanderman, (submitted).

A monoidal DoldKan correspondence for comodules, (submitted).

Rigidification of Connective Comodules, (submitted).
Undergrad and grad projects
MIT
Cofiber Sequences of Thom Spectra over B(ℤ/2)^n, Master thesis advised by Haynes Miller (Fall 2014).
EPFL
Group Cohomology, EPFL Master project supervised by Jacques Thévenaz (Spring 2014).
An Introduction to Stable Homotopy Theory, EPFL Master project supervised by Kathryn Hess (Fall 2013).
The Serre Spectral Sequence (using Dress' construction), EPFL Bachelor project supervised by Kathryn Hess (Spring 2013).
Fiber Bundles in Homotopy Theory (in French), EPFL Bachelor project supervised by Kathryn Hess (Fall 2012).