Department of

# Mathematics

Seminar Calendar
for events the day of Friday, October 11, 2019.

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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, October 11, 2019

2:00 pm in 347 Altgeld Hall,Friday, October 11, 2019

###### See seminar site

Abstract: See seminar site.

3:00 pm in 341 Altgeld Hall,Friday, October 11, 2019

#### An Introduction to Groupoids in Operator Algebras

###### Vincent Villalobos (UIUC Math)

Abstract: This talk will introduce and define groupoids while motivating their importance in operator algebras. We will discuss the various structures that arise within groupoids and then explore the construction of the groupoid $C^\ast$-algebra. Finally, we will discuss the specific case of a Lie groupoid and how the added smooth structure affects the groupoid $C^\ast$-algebra.

4:00 pm in 345 Altgeld Hall,Friday, October 11, 2019

#### "Complex-like" analysis in o-minimal structures (Part 3)

###### Neer Bhardwaj (UIUC)

Abstract: Analogues of many of the basic results in complex analysis can be established over an arbitrary algebraically closed field $K$ of characteristic zero, in the context of an o-minimal expansion of a real closed field $R$, with $K=R[i]$. I will show in particular how one can define winding numbers, and how differentiability begets infinite differentiability in this setting. This expository talk follows the survey given by Lou in the last two weeks and will be based mostly on: "Expansions of algebraically closed fields in o-minimal structures" by Starchenko–Peterzil (https://link.springer.com/article/10.1007/PL00001405)

4:00 pm in Altgeld Hall 245,Friday, October 11, 2019

#### Workshop - how to write a report

###### Alfred Chong and Daniel Linders

4:00 pm in 347 Altgeld Hall,Friday, October 11, 2019

#### Kuratowski 14-Sets Theorem and Related Classifications of Topological Spaces

###### Jinghui Yang (UIUC Math)

Abstract: One very interesting theorem you may encounter when you first study topology is known as the famous Kuratowski 14-sets theorem: Given a topology space (X,T) with T is its topology, for any subset A of X, at most 14 sets can be obtained from A by taking closures and complements. This is really a shocking fact, but even more surprisingly, the “tool” to prove it is rather easy using a strong taste of algebra. Furthermore, this “tool” can be useful to do some basic classification of topology spaces; namely, you can decide the type of some topology spaces completely determined by its “K-Number”. This talk is based on the paper The Kuratowski Closure-Complement Theorem by B.J. Gardner and M. Jackson (2007), published in New Zealand Journal of Mathematics, Vol.38(2008), 9-44. Some basic concepts of topology will be reviewed.

4:00 pm in Altgeld Hall 245,Friday, October 11, 2019