Department of

# Mathematics

Seminar Calendar
for events the day of Friday, September 2, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2016           September 2016          October 2016
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6                1  2  3                      1
7  8  9 10 11 12 13    4  5  6  7  8  9 10    2  3  4  5  6  7  8
14 15 16 17 18 19 20   11 12 13 14 15 16 17    9 10 11 12 13 14 15
21 22 23 24 25 26 27   18 19 20 21 22 23 24   16 17 18 19 20 21 22
28 29 30 31            25 26 27 28 29 30      23 24 25 26 27 28 29
30 31


Friday, September 2, 2016

4:00 pm in 241 Altgeld Hall,Friday, September 2, 2016

#### An Introduction to Algebraic K_1 and K_2

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

Abstract: I'll give a brief introduction to K-theory by recalling the definition of K_0 of a ring and some of its basic properties. Then, I'll define K_1 and K_2 and explain the somewhat surprising fact that these groups fit into a (co)homology theory.

4:00 pm in 345 Altgeld Hall,Friday, September 2, 2016

#### On "Regularity lemma for distal structures" by A. Chernikov and S. Starchenko

###### Anton Bernshteyn (UIUC Math)

4:00 pm in 345 Altgeld Hall,Friday, September 2, 2016

#### On "Regularity lemma for distal structures" by A. Chernikov and S. Starchenko: Prologue

###### Anton Bernshteyn (UIUC Math)

Abstract: Motivated by problems in discrete geometry, Alon, Pach, Pinchasi, Radoi\v ci\' c, and Sharir (2005) established a strong version of the bipartite Ramsey theorem for semialgebraic graphs: any such graph or its complement contains a complete bipartite subgraph with parts of linear size. Eventually, this result led to a generalization due to Chernikov and Starchenko (2015), who extended it to graphs definable in distal structures. In this series of talks, we are planning to give an overview of the Chernikov--Starchenko result. In this first introductory talk we will review the story behind the work of Alon \emph{et al.}, give a rough sketch of their proof, and see the seeds of model theory in it. We will also mention some further results, such as the strong Szemer$\text{\'e}$di regularity lemma for semialgebraic / distal hypergraphs.

4:00 pm in 345 Altgeld Hall,Friday, September 2, 2016

#### On "Regularity lemma for distal structures" by A. Chernikov and S. Starchenko: Prologue

###### Anton Bernshteyn (UIUC Math)

Abstract: Motivated by problems in discrete geometry, Alon, Pach, Pinchasi, Radoičić, and Sharir (2005) established a strong version of the bipartite Ramsey theorem for semialgebraic graphs: any such graph or its complement contains a complete bipartite subgraph with parts of linear size. Eventually, this result led to a generalization due to Chernikov and Starchenko (2015), who extended it to graphs definable in distal structures. In this series of talks, we are planning to give an overview of the Chernikov–Starchenko result. In this first introductory talk we will review the story behind the work of Alon et al., give a rough sketch of their proof, and see the seeds of model theory in it. We will also mention some further results, such as the strong Szemerédi regularity lemma for semialgebraic / distal hypergraphs.

4:00 pm in 243 Altgeld Hall,Friday, September 2, 2016

#### Polynomials for symmetric orbit closures on the flag variety

###### Benjamin Wyser   [email] (UIUC Math)

Abstract: The variety of complete flags has many interesting subvarieties. The most famous are the Schubert varieties. In 1982, Lascoux and Sch\"{u}tzenberger defined Schubert polynomials as natural representatives of their cohomology classes. These polynomials have been studied extensively using a wide range of tools from combinatorics, representation theory and algebraic geometry. In the representation theory of real Lie groups, one finds analogues of the Schubert varieties. These are the closures of orbits on the flag variety under the action of a certain symmetric subgroup. I will discuss joint work with Alexander Yong in which we compute analogues of Schubert polynomials in this setting. I will describe the computation and also discuss some combinatorial and geometric properties of our polynomials.