My research is in the area of algebraic topology known as stable homotopy theory, in connection with algebraic Ktheory, higher category theory and theoretical computer science. I am particularly interested in showing how certain algebraic structures lead to new and effective computations. For instance, I have shown that model categories fail to accurately represent socalled coalgebraic structures in stable homotopy theory, and hence we need the language of ∞categories to accurately capture homotopy coherent structures. More recently, I have studied trace methods to compute algebraic Ktheory and introduced new variants of topological Hochschild homology. I have also extended my interests to theoretical computer science, applying methods of category theory and coalgebras to study algebraic data type interactions.
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 (Aug 2020).
4
Preprints

Equivariant algebraic Ktheory of symmetric monoidal Mackey functors, with Maxine Calle and David Chan, (submitted)

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).