Upcoming Talks

In Spring 2025, the UChicago Algebraic Topology Seminar will meet on Tuesdays at 4:00-5:00PM in Eckhart Hall 206 and will be preceded by a pretalk 3:30-4PM (unless otherwise noted).

To receive emails about the seminar, please email Nikolai Konovalov requesting to be subscribed to our mailing list.

• • Apr 012025

  Anish Chedalavada (Johns Hopkins University)

  Geometries, Tensor-Triangular Geometry, and the Reconstruction of Schemes

  In this talk I will present joint work with Aoki-Barthel-Schlank-Stevenson on reinterpreting standard constructions and results of tt-geometry in terms of the framework of geometrically structured topoi, following Lurie's approach to derived algebraic geometry. The first part of the talk will provide as an introduction to this framework and a presentation of the standard definitions of classical Zariski and (following tt-geometry) higher Zariski geometry. In the second part of the talk, I will present followup independent work which reinterprets the scheme-theoretic reconstruction results of Balmer-Neeman-Thomason for qcqs schemes in terms of the framework of relative geometry; this will apply in particular to nonconnective spectral schemes and provide a universal property for their categories of perfect complexes. Time permitting, we will indicate an application to the construction of spectral enhancements of classical support varieties, as well as a simple application to torsion-free groups of endotrivial modules at the prime 2.

If you have any questions, please contact Toni Annala, Nikolai Konovalov, Akhil Mathew, Tomer Schlank, or Peter May.