Department of

# Mathematics

Seminar Calendar
for events the day of Friday, February 18, 2022.

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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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Friday, February 18, 2022

1:00 pm in Altgeld Hall 147,Friday, February 18, 2022

#### An introduction to p-adic analysis

###### Robert J. Dicks (UIUC)

Abstract: This talk is meant to be an introduction p-adic number and p-adic analysis. These arise via completing the rational numbers using a metric (relative to a prime number p) which is very different from the ordinary euclidean metric. The first part of the talk will introduce this number system and focus on ways in which it differs from our "Euclidean" intuition. We then will discuss p-adic integration. We will then define the p-adic zeta function. The goal will be to describe (without proof) how these are related to the Riemann zeta function. This talk is aimed at 1st year graduate students.

3:00 pm in 341 Altgeld Hall,Friday, February 18, 2022

#### Formalism of six operations and derived algebraic stacks

###### Timmy Feng (UIUC Math)

Abstract: The formalism of six operations was originally introduced by A.Grothendieck and his collaborators in the study of \'etale cohomology. It naturally leads to many well-known results in cohomology theory like duality and Lefschetz trace formula. This partially justifies the slogan that the formalism of six operations are enhanced cohomology theories. In this talk, I will introduce the formalism of six operations. I will explain the relation between it and some cohomology theories (Topological, coherent, l-adic). Moreover, I will talk about the application of it to a nice class of derived algebraic stacks. And show that this leads to some nontrivial results of algebraic (homotopy) K-theory for stacks.

4:00 pm in 347 Altgeld Hall,Friday, February 18, 2022

#### An Advert for Generalized Complex Geometry

###### Sambit Senapati (UIUC)

Abstract: For many years physicists and mathematicians have studied the mysterious links between complex and symplectic geometry predicted by mirror symmetry. Generalized Complex geometry is a framework explicitly unifying complex and symplectic geometry and is hoped to allow for a formulation of this curious bridge. It is however interesting in its own right, as a differential geometric framework generalizing and specializing other differential geometric settings. I will try to give a broad introduction to this topic, focusing on an overview rather than on details. In particular, I’ll talk about concepts from symplectic and complex geometry that extend to GC structures as well as aspects that are unique to it.