Department of

# Mathematics

Seminar Calendar
for events the day of Monday, November 30, 2015.

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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 30, 2015

4:00 pm in 141 Altgeld Hall,Monday, November 30, 2015

#### "Topological dynamics of closed subgroups of $S_\infty$" by Andy Zucker

###### Hamed Khalilian

Abstract: In this and the following talks, I will present some parts of the paper mentioned in the title. In this talk, I will cover some preliminaries and a new proof of the Kechris-Pestov-Todorsevich correspondence.

4:00 pm in 145 Altgeld Hall,Monday, November 30, 2015

#### Hilbert schemes of points on $\mathbb{C}^2$ as hyperkahler quotients

###### Shiyu Shen (UIUC Math)

Abstract: I will talk about why the Hilbert-Chow morphism from $(\mathbb{C}^2)^{[n]}$ to $Sym^n(\mathbb{C}^2)$ is a map between hyperkahler quotients, and how to generalize this construction to ADHM moduli spaces.

4:00 pm in 245 Altgeld Hall,Monday, November 30, 2015

#### Commutative Algebra and Combinatorics

###### Hal Schenck (Department of Mathematics, University of Illinois)

Abstract: This talk will give an overview of the spectacular success of algebraic methods in studying problems in discrete geometry and combinatorics. First we'll discuss the face vector (number of vertices, edges, etc.) of a convex polytope and recall Euler's famous formula for polytopes of dimension 3. Then we'll discuss graded rings, focusing on polynomial rings and quotients. Associated to a simplicial polytope P (every face is "like" a triangle) is a graded ring called the Stanley-Reisner ring, which "remembers" everything about P, and gives a beautiful algebra/combinatorics dictionary. I will sketch Stanley's solution to a famous conjecture using this machinery, and also touch on connections between P and objects from algebraic geometry (toric varieties).

5:00 pm in 241 Altgeld Hall,Monday, November 30, 2015