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.

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 .