Jonathan Beardsley

Research     Teaching     Other

Most of my papers are available on the arXiv here. We have an informal seminar here at UNR on topics related to homotopical algebra, broadly construed. The website is here. Please contact me if you'd like to attend.

Research Papers

  • Projective Geometries and Simple Pointed Matroids as 𝔽₁-modules, with So Nakamura. Submitted (arXiv).
  • Brauer Wall Groups and Truncated Picard Spectra of K-theory, with Kiran Luecke and Jack Morava. Submitted (arXiv).
  • Labeled Cospan Categories and Properads, with Philip Hackney. Published in Journal of Pure and Applied Algebra (arXiv).
  • Skeleta and categories of algebras, with Tyler Lawson. Submitted (arXiv).
  • On Bialgebras, Comodules, Descent Data and Thom Spectra in ∞-categories. Forthcoming in Homology, Homotopy and Applications (arXiv).
  • Koszul duality in Higher Topoi, with Maximilien Péroux. Published in Homology, Homotopy and Applications (arXiv).
  • The Operadic Nerve, Relative Nerve, and the Grothendieck Construction, with Liang Ze Wong. Published in Theory and Applications of Categories (arXiv).
  • The Enriched Grothendieck Construction, with Liang Ze Wong. Published in Advances in Mathematics (arXiv).
  • Toward a Galois Theory of the Integers Over the Sphere Spectrum, with Jack Morava. Published in Journal of Geometry and Physics (arXiv).
  • A Theorem on Multiplicative Cell Attachments with an Application to Ravenel's X(n) Spectra. Published in Journal of Homotopy and Related Structures (arXiv).
  • Relative Thom Spectra Via Operadic Kan Extensions. Published in Algebraic and Geometric Topology (arXiv).
  • A Sheaf of Boehmians, with Piotr Mikusinski. Published in Annales Polonici Mathematici (arXiv).
  • Other Writing

  • Matroids as 𝔽₁-modules Notes from a talk given in the UC-Irvine Algebra Seminar.
  • Group Theory for ∞-Groups Notes from a talk given in the UIUC Topology Seminar.
  • Picard Spaces and Orientations: Notes from an expository talk on Picard spaces given at the ``Chromatic Nullstellensatz Seminar."
  • Toward Higher Algebra over 𝔽₁: Notes from a talk at the conference "Low Dimensional Topology and Number Theory" at Kyushu University.
  • Interpretations of the Truncated Picard Spectra of KO and KU: Notes from a talk given at the BIRS workshop "Cobordisms, Strings and Thom Spectra," held at the Casa Matématica Oaxaca.
  • On Braids and Cobordism Theories: Notes from a talk given in University of Glasgow's topology seminar.
  • 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 Topological 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.

    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.