Speaker: Mark Behrens
University of Notre Dame
Will give a Topology Seminar entitled:
Synthetic spectra
Abstract: Synthetic spectra (aka filtrered spectra) are a way of forming a homotopy theoretic object that encodes a spectral sequence. The resulting objects have bigraded homotopy groups from which you can read off the spectral sequence. In this way they can be thought of as a kind of replacement for a spectral sequence, but also give a way of building new spectral sequences from old ones (e.g. you get a triangulated category of "spectral sequences"). The crazy thing is that such categories are known by work of Gheorghe-Wang-Xu, Gheorghe-Isaksen-Krause-Ricka, Pstragowski, and Burkland-Hahn-Senger, to give models of the motivic homotopy categories over C and R. I'll describe this connection. Despite the tenor of this abstract, this is meant to be an expository talk, and I will define everything.
Date: 09-10-2024
Time: 2:30 pm
Location: 258 Hurley