Jonathan Beardsley

Research     Teaching     Other

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 .