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
Some Galois Theory for Bordism Homology given in the UNR Mathematics and Statistics Colloquium.
On the PROB of Singular Braids given at The Third Conference on Operad Theory and Related Topics .
Symmetry, Topology and the Nobel Prize, slides for an expository talk on topological phases of matter.
Twisted Forms in Homotopy Theory.
Bialgebras in Spectra .