[Binghamton Geometry Topology Seminar] GT Seminar: Bastiaan Cnossen

[Jose Roman Aranda Cuevas]

Hi everyone,

This week we are pleased to have Bastiaan Cnossen (MPI / U Bonn) speaking
about traces and categorification, title, and abstract below. As usual, the
talk will be TODAY, Thursday at 2:50 pm in WH 100E.

This will be a *virtual talk*, but we'll project it in WH 100E for those
who want to come. In case you can't make it and would like to join
remotely, you can join at the link:

https://binghamton.zoom.us/j/94800072611

We'll also gather for lunch at 12pm just outside WH100E. See you there!

Best,
Cary and Roman

=========================================
*Title:* Traces and categorification
*Abstract:* The trace of a linear operator is simple to define, yet appears
all over mathematics in many disguises: from characters of representations,
through fixed-point formulas, to various geometric transfer maps. The
theory of oo-categories and higher algebra allows one to organize many of
these occurrences of the trace within a formal unified calculus. This
calculus is more intricate and elaborate than one might expect, because
some of its fundamental features are revealed only by /categorification/,
leading to investigations of traces in (oo,2)-categories.

In this talk, I will describe joint work with Shachar Carmeli, Maxime Ramzi
and Lior Yanovski that sets up a general "character theory" for studying,
among other things, the interaction of traces with colimits by an "induced
character formula" (generalizing and refining work of Ponto-Shulman). The
interaction between traces and categorification plays a key role in our
approach. I will also explain how this theory can be applied to the study
of the Becker-Gottlieb transfer and of topological Hochschild homology of
Thom spectra.
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