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.

## Published and Submitted Papers

**Koszul Duality in Higher Topoi,** with M. Péroux, *Submitted*. arXiv
**The Operadic Nerve, Relative Nerve, and the Grothendieck Construction** with L.Z. Wong,
*Theory and Applications of Categories*, 34 (2019), Paper No. 13, 349–374. arXiv
**The Enriched Grothendieck Construction**, with L.Z. Wong, *Advances in Mathematics* 344 (2019), 234–261. arXiv
**A Theorem on Multiplicative Cell Attachments with an Application to Ravenel's X(n) Spectra**, *Journal of Homotopy and Related Structures* 14-3 (2019), 611–624. arXiv
**Toward a Galois Theory of the Integers Over the Sphere Spectrum**, with J. Morava,
*Journal of Geometry and Physics* 131 (2018), 41–51. arXiv
**Relative Thom Spectra Via Operadic Kan Extensions**, *Algebraic and Geometric Topology* 17-2 (2017), 1151–1162. arXiv
**A Sheaf of Boehmians, with Piotr Mikusinski**, *Annales Polinici Mathematici* 107 (2013), 293–307. arXiv
## Preprints and Other Writing

** Thom Objects are Cotorsors:** A preprint describing work in progress to better understand the coalgebraic structure on homotopical quotient objects.
**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 .