Research Writing
Publications & Preprints
A chromatic vanishing result for TR. Joint with Jonas 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]
In Preparation
Cyclotomic spectra associated to nonunital algebras in bimodules.
Associated to a pair (A,I) where A is a ring spectrum and I is a nonunital algebra in (A,A)-bimodules, I construct a cyclotomic spectrum denoted by T(A,I). This construction recovers two well-known examples of cyclotomic spectra: (1) THH of a trivial square zero extension and (2) the fiber of the map THH(A)->THH(B) induced by an idempotent extension of ring spectra.
Lax monoidality of the oo-categorical Dold-Kan correspondence (joint with Maximilien Peroux).
We show that for C a small symmetric monoidal category with finite colimits and whose tensor product is compatible with finite colimits, the formation of the skeletal filtration of simplicial objects in C is lax symmetric monoidal. Hopefully, we will have something interesting to say about the cosimplicial case sometime in the future.
Ongoing projects
Real analogues of continuous cohomology (joint with Myungsin Cho, Teena Gerhardt, Juan Moreno, and J.D. Quigley).
We are trying to understand the "real" analogue of the continuous homology spectral sequence considered by Bruner--Rognes, both conceptually and computationally.
Notes and misc. writing
Hopefully something will appear here soon!
I used to have two documents linked here, but I decided to take them down. If for some reason you would like access to either of them, please email me.