I'm broadly interested in algebraic and homotopical structure in topology and geometry. I have ongoing work in the following areas: derived noncommutative algebra and geometry; cobordism theories; operads, ∞-operads; enriched category theory; representations of braid groups.
Most of my papers are available on the arXiv here.

## Research Papers

**Thom Objects are Cotorsors**: arXiv
**The Operadic Nerve, Relative Nerve, and the Grothendieck Construction**: arXiv
**The Enriched Grothendieck Construction, with Liang Ze Wong **: Forthcoming in *Adv. in Math.* Available at arXiv
**Toward a Galois Theory of the Integers Over the Sphere Spectrum, with Jack Morava **: Published in Volume 131 of the *J. of Geometry and Physics*. arXiv
**A Theorem on Multiplicative Cell Attachments with an Application to Ravenel's X(n) Spectra**: Forthcoming in *J. Homotopy Rel. Struct.* Available at arXiv
**Relative Thom Spectra Via Operadic Kan Extensions**: Published in *Algebraic and Geometric Topology* 17-2. arXiv
**A Sheaf of Boehmians, with Piotr Mikusinski**: Published in Vol. 107 of *Ann. Pol. Mathematici.* arXiv
## Other Writing

**A User's Guide: Relative Thom Spectra via Operadic Kan Extensions:** An exposition of the main ideas in my paper "Relative Thom Spectra via Operadic Kan Extensions," accessible to graduate students studying homotopy theory.
**Notes on Lubin-Tate Cohomology:** Some notes about the cohomology of a complex that comes up in deformations of formal groups as well as extensions of n-buds.
**THH of X(n):** A computation of the Topopological Hochschild Homology of Ravenel's X(n) spectra.
**The Harmonic Bousfield Lattice:** A computation of the Bousfield lattice of the category of p-local harmonic spectra. The main theorem and proof were used by Luke Wolcott here.
**Laysplanations:** Borrowing a term from Piper Harron, some of my non-technical writing on mathematics is available here.
I've written a few articles for Eric Peterson's math blog Chromotopy which you can find here.
## Talk Slides

Symmetry, Topology and the Nobel Prize, slides for an expository talk on topological phases of matter.
Twisted Forms in Homotopy Theory.
Bialgebras in Spectra .