Department of

Mathematics


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

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Questions regarding events or the calendar should be directed to Tori Corkery.
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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.