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