Department of

# Mathematics

Seminar Calendar
for events the day of Monday, November 5, 2018.

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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, November 5, 2018

12:00 pm in Altgeld Hall 102,Monday, November 5, 2018

#### 2FA Open Hour

###### Math IT   [email] (Illinois Math)

Abstract: If you have any questions regarding the mandatory 2FA enrollment, require a 2FA token, or need help setting up the Duo Mobile app, please stop by our office, 102 Altgeld Hall, from noon to 1pm. If none of our early-November open hours work for you, please contact us at math-it@illinois.edu.

2:00 pm in 343 Altgeld Hall,Monday, November 5, 2018

#### $\ell^2$ Betti numbers of countable Borel equivalence relations: Part 2

###### Ruiyuan (Ronnie) Chen (UIUC Math)

Abstract: We will discuss Gaboriau's 2002 paper "Invariants $\ell^2$ de relations d'équivalence et de groupes" from a descriptive set-theoretic point of view. In this second talk, we will discuss Borel fields of sets and structures (in particular, simplicial complexes and Hilbert spaces) over a countable Borel equivalence relation, and how to measure their "Borel cardinality" using Tarski's theory of cardinal algebras.

3:00 pm in 345 Altgeld Hall,Monday, November 5, 2018

#### Witt groups and Real K-theory

###### Daniel Carmody (UIUC Math)

Abstract: Swan's theorem gives an equivalence of categories between vector bundles on a manifold and finitely-generated projective modules over the ring of continuous functions on the manifold. I'll discuss a variant of this theorem for vector bundles on a manifold with the additional data of a non-degenerate symmetric bilinear form.

4:00 pm in 245 Altgeld Hall,Monday, November 5, 2018

#### Extremal problems on cycles and paths in dense graphs and hypergraphs

###### Alexandr Kostochka   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: A typical extremal problem in graph theory is: how many edges may have a simple n-vertex graph that does not have cycles or paths with lengths in a given set? Similar problems are important for hypergraphs for different definitions of cycles and paths (note that one can define paths and cycles in hypergraphs in several ways). We discuss some problems of this kind and recent progress on them.

5:00 pm in 241 Altgeld Hall,Monday, November 5, 2018

#### Noncommutative Talagrand inequality

###### Marius Junge (UIUC)

Abstract: We wll show how formulate and proof mareix valued versions of Talagrand type concentration inequalities.