Department of

# Mathematics

Seminar Calendar
for events the day of Monday, October 19, 2020.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, October 19, 2020

3:00 pm in Zoom,Monday, October 19, 2020

#### An Introduction to Algebraic $K$-Theory

###### Brian Shin (UIUC)

Abstract: In this expository talk I'd like to give a brief introduction to algebraic $K$-theory. We'll start with an short historical overview. We'll then go into one of the many successful definitions for higher algebraic $K$-theory, that given by Waldhausen. If time permits, I'll give a slightly more conceptual perspective on Waldhausen $K$-theory. Please email vb8 at illinois dot edu for the zoom details.

3:00 pm in zoom,Monday, October 19, 2020

#### Frobenius objects in categories of relations and spans

###### Rajan Mehta (Smith College)

Abstract: Frobenius algebras can be given a category-theoretic definition in terms of the category of vector spaces. This leads to a more general definition of Frobenius object in any monoidal category. In this talk, I will describe Frobenius objects in categories where the objects are sets and the morphisms are relations or spans. These categories can be viewed as toy models for the symplectic category. The main result is that, in both cases, it is possible to construct a simplicial set that encodes the data of the Frobenius structure. This work is a very small first step in a bigger program aimed at better understanding the relationship between Poisson geometry and two-dimensional topological field theory. Part of the talk will be devoted to giving an overview of this question as well as its analogue in dimension 3. This is based on work with Ruoqi Zhang and work in progress with Ivan Contreras and Molly Keller.