Araminta Amabel, Qingyuan Bai, Clark Barwick, Magnus Carlson, Vladimir Chugunov, Arun Debray, Sanath Devalapurkar, Sergei Fomin, Saul Glasman, Victor Guillemin, Tim Holzschuh, Marcin Lara, Catrin Mair, Louis Martini, Guglielmo Nocera, Mauro Porta, Piotr Pstrągowski, Maxime Ramzi, Ravi Shankar, Jan Steinebrunner, Jean-Baptiste Teyssier, Marco Volpe, Sebastian Wolf
Proves representability results for derived moduli stacks of constructible and perverse sheaves. Previously, weaker versions of these results appeared in Exodromy beyond conicality. This paper has stronger results and is self-contained (using exodromy as a black box).
Proves that for a spectral ∞-topos (e.g., the étale ∞-topos of a qcqs scheme), the classifying anima of its condensed ∞-category of all points (introduced by Lurie) and its condensed ∞-category of coherent points (introduced in our work with Barwick–Glasman) agree.
To appear in Selecta Mathematica
To appear in the Journal of Topology
Generalizes the exodromy equivalence in topology beyond the setting of conically stratified spaces, with a number of applications.
To appear in Algebraic and Geometric Topology
Initially posted here in November 2022, but wasn't uploaded to the arXiv until May 2024.
Doc. Math. 26 (2021), 1423–1464.
[pdf, arXiv:1912.04130, Journal version]
We prove the James and Hilton–Milnor Splittings in a very general context that applies to motivic spaces over an arbitrary base. We also give a new, non-computational proof of the metastable EHP sequence in an ∞-topos that essentially only makes use of the Blakers–Massey Theorem.
To appear in Annales scientifiques de l'École normale supérieure.
To be published in Cambridge Studies in Advanced Mathematics.
We give an overview of differential cohomology from a modern, homotopy-theoretic perspective in terms of sheaves on manifolds. Although modern techniques are used, we base our discussion in the classical precursors to this modern approach, such as Chern–Weil theory and differential characters, and include the necessary background to increase accessibility. Special treatment is given to differential characteristic classes, including a differential lift of the first Pontryagin class. Multiple applications, including to configuration spaces, invertible field theories, and conformal immersions, are also discussed. This book is based on talks given at MIT’s Juvitop seminar run jointly with UT Austin in the Fall of 2019.
In addition to chapters by the editors, there are chapters by: Dexter Chua, Sanath Devalapurkar, Dan Freed, Mike Hopkins, Greg Parker, Charlie Reid, and Adela Zhang.
The material here now includes the contents of the four papers [arXiv:1812.11637, pdf], [arXiv:1901.09414, pdf], [arXiv:1904.01877, pdf], and [arXiv:1904.09966, pdf].
World Scientific Publishing Company, March 2019, ISBN: 9789813272774. DOI: 10.1142/11058.
Oberwolfach Reports: Homotopy Theory August 2019