Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, September 2, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, September 2, 2014

1:00 pm in Altgeld Hall 243,Tuesday, September 2, 2014

Counting non-simple closed curves on surfaces

Jenya Sapir (UIUC Math)

Abstract: We show how to get coarse bounds on the number of (non-simple) closed geodesics on a surface, given upper bounds on both length and self-intersection number. Recent work by Mirzakhani and by Rivin has produced asymptotics for the growth of the number of simple closed curves and curves with one self-intersection (respectively) with respect to length. However, no asymptotics, or even bounds, were previously known for other bounds on self-intersection number. Time permitting, we will discuss some applications of this result. A video recording of this talk can be found at http://gear.math.illinois.edu/events/Geometry-Groups-Dynamics-GEAR-Seminar.html

1:00 pm in 345 Altgeld Hall,Tuesday, September 2, 2014

Regular cross-sections of Borel flows

Kostya Slutsky (UIC)

Abstract: A cross-section of a Borel flow is a Borel set that has countable intersection with each orbit of the flow. We shall be interested in constructing cross-sections with a prescribed set of possible distances between adjacent points within orbits. The main result of the talk is that given any two rationally independent positive reals and a free Borel flow one can always find a cross-section with distances between adjacent points being only these two real numbers. We shall give an overview of the subject from both ergodic theoretical and descriptive points of view and an application of the above result to orbit equivalence of flows will be presented.

1:00 pm in 347 Altgeld Hall,Tuesday, September 2, 2014

Invariant Gibbs Measures and Hamiltonian PDEs

Samantha Xu (UIUC Math)

Abstract: Liouville's Theorem says that the flow of a Hamiltonian ODE preserves Lebesgue measure, and a corresponding Gibbs measure as well. This notion can be generalized to infinite dimensional systems for various Hamiltonian PDEs. In this talk, we will discuss the role of randomization on initial datum, methods of constructing an invariant Gibbs measure, and some recent results.

3:00 pm in 241 Altgeld Hall,Tuesday, September 2, 2014

On the applications of counting independent sets in hypergraphs

Jozsef Balogh   [email] (UIUC Math)

Abstract: Recently, Balogh-Morris-Samotij and Saxton-Thomason developed a method of counting independent sets in hypergraphs. During the talk, I show a recent application of the method; solving the following Erdos problem: What is the number of maximal triangle-free graphs? If there is some extra time in the talk, I will survey some other recent applications. Note that despite similar abstracts in the past, the talk is significantly new. These applications are partly joint with Shagnik Das, Michelle Delcourt, Hong Liu, Richard Mycroft, Sarka Petrickova, Maryam Sharifzadeh and Andrew Treglown.