Department of

Mathematics


Seminar Calendar
for events the day of Monday, September 25, 2017.

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Monday, September 25, 2017

3:00 pm in 141 Altgeld Hall,Monday, September 25, 2017

An Invitation to Motivic Homotopy Theory

Daniel Carmody   [email] (UIUC)

Abstract: In this talk Iíll introduce some of the basic constructions in motivic homotopy theory while trying to give motivations for some of the more complex definitions. This will be largely based on Dan Duggerís $Universal$ $Homotopy$ $Theories$ paper.

4:00 pm in 245 Altgeld Hall,Monday, September 25, 2017

Rigidity in orbit equivalence via cost

Anush Tserunyan   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: The talk is tailored around the following basic question: Let $\mathbb{F}_n$↷$[0,1]$ and $\mathbb{F}_m$↷$[0,1]$ be free actions of the free groups on $n$ and $m$ generators and assume that these actions preserve the Lebesgue measure and are ergodic (a bunch of words you're not supposed to know—ignore). If these actions produce the same orbits (i.e. their orbit equivalence relations are equal), must it be that $n = m$? This is an instance of the more general question: how much of the group is "remembered" by the orbit equivalence relations of its free actions? The phenomenon of a weaker notion "remembering" a stronger one is referred to as rigidity. We will describe the answer to the initial question (due to D. Gaboriau) by introducing an invariant called cost, which is tied to measurable graphs and combinatorics, and even ideas from homology theory. I will only assume familiarity with the words graph and measure.