Department of

Mathematics


Seminar Calendar
for Logic Seminar events the year of Tuesday, October 20, 2020.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, January 21, 2020

1:00 pm in 241 Altgeld Hall,Tuesday, January 21, 2020

Organizational meeting

Abstract: Just a short organizational meeting for Logic seminar and the MT/DST Seminar.

Tuesday, February 11, 2020

1:00 pm in 241 Altgeld Hall,Tuesday, February 11, 2020

The Borel complexity of quotient groups

Joshua Frisch (Caltech Math)

Abstract: The theory of Borel equivalence relations gives us rigorous methods to says when one classification problem/equivalence relation is more "complicated" than another. Given a countable group it's outer-automorphism group naturally has the structure of a borel equivalence relation. Motivated by this example, in this talk I will give a brief introduction to the theory of countable borel equivalence relations, describe some previously known connections with the theory of groups and, finally, describe a new new result explaining exactly how complicated the Borel complexity of quotient groups (which generalize outer-automorphism groups) can be. This is joint work with Forte Shinko.

Tuesday, March 24, 2020

1:00 pm in https://illinois.zoom.us/j/249415194,Tuesday, March 24, 2020

Borel structures on the space of left orderings

Filippo Calderoni (UIC Math)

Abstract: In this talk I will present some recent results on left-orderable groups and their interplay with descriptive set theory. We shall discuss how Borel classification can be used to analyze the space of left-orderings of a given countable group modulo the conjugacy action. In particular we shall see that if G is a countable nonabelian free group, then the conjugacy relation on its space of left orderings is a universal countable Borel equivalence relation. This is joint work with A. Clay.

Friday, April 3, 2020

3:00 pm in https://illinois.zoom.us/j/521113604 (email Anush Tserunyan for the password),Friday, April 3, 2020

A dynamical obstruction for classification by actions of TSI Polish groups

Aristotelis Panagiotopoulos (Caltech Math)

Abstract: A big part of mathematical activity revolves around classification problems. However, not every classification problem has a satisfactory solution, and some classification problems are more complicated than others. Dynamical properties such as generic ergodicity and turbulence are crucial in the development of a rich complexity theory for classification problems. In this talk we will review some of the existing anti-classification techniques and we will introduce a new obstruction for classification by orbit equivalence relations of TSI Polish groups; a topological group is TSI if it admits a compatible two side invariant metric. We will then show that the Wreath product of any two non-compact subgroups of $S_{\infty}$ admits an action whose orbit equivalence relation is generically ergodic with respect to orbit equivalence relations of TSI group actions.
This is joint work with Shaun Allison.

Tuesday, April 21, 2020

1:00 pm in https://illinois.zoom.us/j/422077317 (email Anush Tserunyan for the password),Tuesday, April 21, 2020

The universal theory of random groups

Meng-Che (Turbo) Ho (Purdue University)

Abstract: Random groups are proposed by Gromov as a model to study the typical behavior of finitely presented groups. They share many properties of the free group, and Knight asked if they also have the same first-order theory as the free group. In this talk, we will discuss a positive result for the first step toward this question, namely the universal theory of random groups. The main tools we use are the machinery developed in Sela’s solution to the Tarski problem.
This is joint work with Remi Coulon and Alan Logan.

Wednesday, October 14, 2020

1:00 pm in Zoom (email ruiyuan at illinois for info),Wednesday, October 14, 2020

A backward ergodic theorem and its forward implications

Jenna Zomback (UIUC Math)

Abstract: A pointwise ergodic theorem for the action of a transformation $T$ on a probability space equates the global property of ergodicity of the transformation to its pointwise combinatorics. Our main result is a backward (in the direction of $T^{-1}$) ergodic theorem for countable-to-one probability measure preserving (pmp) transformations $T$. We discuss various examples of such transformations, including the shift map on Markov chains, which yields a new (forward) pointwise ergodic theorem for pmp actions of finitely generated countable groups, as well as one for the (non-pmp) actions of free groups on their boundary. This is joint work with Anush Tserunyan.