Research interests
I study homotopy theory, and am broadly interested the application of homotopical techniques to related areas. Some major themes of my work include:
Cobordism and derived geometry.
Trace methods in algebraic K-theory.
Multiplicative filtrations in category theory and stable homotopy theory.
On Real homological trace methods. Joint with Cho, Gerhardt, Moreno, Quigley. [arXiv:2608.04297] submitted.
A homotopy coherent Pontryagin--Thom isomorphism. Joint with Blakey.
[arXiv:2607.01482] submitted.
On products of skeleta. Joint with Peroux.
[arXiv:2510.18961] submitted.
A chromatic vanishing result for TR. Joint with McCandless.
[Proc. Amer. Math Soc. 152, (2024), 3705-3713]
The May filtration on THH and faithfully flat descent.
[Journal of Pure and Applied Algebra, Volume 229, Issue 1, January 2025]
Multiplicative properties of skeletal filtrations. A multi-part project studying a homotopy coherent Alexander--Whitney map (joint with Lawson and Peroux) and other flavors of skeletal filtrations (joint with Peroux).
Traces and cyclotomic spectra. Using the structure of THH as a cyclic trace theory, I construct a cyclotomic spectrum associated to a ring spectrum A and a nonunital A-algebra J. This is closely related to the THH of a trivial square-zero extension.
"Locally unipotent Z-actions" in Arbeitsgemeinschaft: Algebraic K-theory and the Telescope Conjecture.
[Oberwolfach Report No. 47/2024]