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Topological Hochschild homology of X(n)

- Jonathan Beardsley
- Mathematics
- 30 August 2017

We show that Ravenel's spectrum $X(2)$ is the versal $E_1$-$S$-algebra of characteristic $\eta$. This implies that every $E_1$-$S$-algebra $R$ of characteristic $\eta$ admits an $E_1$-ring map… Expand

Relative Thom Spectra Via Operadic Kan Extensions

- Jonathan Beardsley
- Mathematics
- 16 January 2016

We show that a large number of Thom spectra, i.e. colimits of morphisms $BG\to BGL_1(\mathbb{S})$, can be obtained as iterated Thom spectra, i.e. colimits of morphisms $BG\to BGL_1(Mf)$ for some Thom… Expand

A User's Guide: Relative Thom Spectra via Operadic Kan Extensions

- Jonathan Beardsley
- Mathematics
- 21 September 2017

This is an expository paper about the paper Relative Thom Spectra via Operadic Kan Extensions.

The Operadic Nerve, Relative Nerve, and the Grothendieck Construction

- Jonathan Beardsley, Liang Ze Wong
- Mathematics
- 24 August 2018

We relate the relative nerve $\mathrm{N}_f(\mathcal{D})$ of a diagram of simplicial sets $f \colon \mathcal{D} \to \mathsf{sSet}$ with the Grothendieck construction $\mathsf{Gr} F$ of a simplicial… Expand

The enriched Grothendieck construction

- Jonathan Beardsley, Liang Ze Wong
- MathematicsAdvances in Mathematics
- 11 April 2018

Coalgebraic Structure and Intermediate Hopf-Galois Extensions of Thom Spectra in Quasicategories

- Jonathan Beardsley
- Mathematics
- 22 March 2016

We extend Lurie’s work on derived algebraic geometry to define highly structured En-coalgebras, bialgebras and comodules in the homotopy theorist’s category of spectra. We then show that… Expand

Toward a Galois Theory of $S^0\to\mathbb{Z}$

- Jack Morava, Jonathan Beardsley
- Mathematics
- 16 October 2017

Notes from a talk at the Fudan Conference on noncommutative geometry, in honor of Alain Connes' 70th birthday: we summarize some classic work on Eilenberg MacLane spectra in terms of more recent work… Expand

Skeleta and categories of algebras

- Jonathan Beardsley, T. Lawson
- Mathematics
- 18 October 2021

We define a notion of a connectivity structure on an ∞-category, analogous to a t-structure but applicable in unstable contexts—such as spaces, or algebras over an operad. This allows us to… Expand

Labelled cospan categories and properads

- Jonathan Beardsley, Philip Hackney
- Mathematics
- 1 June 2022

We prove Steinebrunner’s conjecture on the biequivalence between (colored) properads and labelled cospan categories. The main part of the work is to establish a 1-categorical, strict version of the… Expand

Koszul Duality in Higher Topoi

- Jonathan Beardsley, Maximilien P'eroux
- Mathematics
- 25 September 2019

We show that for any pointed and $k$-connective object $X$ of an $n$-topos $\mathcal{X}$ for $0\leq n\leq\infty$ and $k>0$, there is an equivalence between the $\infty$-category of modules in… Expand

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