Department of

Mathematics


Seminar Calendar
for Descriptive Set Theory Seminar events the year of Monday, February 11, 2019.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2019          February 2019            March 2019     
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Wednesday, January 30, 2019

3:00 pm in 341 Altgeld Hall,Wednesday, January 30, 2019

The cube problem and Schroeder-Bernstein problem for linear orders

Garret Ervin (Carnegie Mellon)

Abstract: We sketch proofs of solutions to two old problems posed by Sierpinski concerning products of linear orders. The first problem asks whether there exists a linear order $X$ that is isomorphic to its lexicographic cube but not to its square; the second, whether there are two non-isomorphic orders $Y$ and $Z$ that divide each other on both the left and right side. For other classes of structures, the corresponding questions are usually either both positive or both negative, but for linear orders the answers diverge: there is no such $X$, but there are such $Y$ and $Z$.

Wednesday, February 6, 2019

3:00 pm in 341 Altgeld Hall,Wednesday, February 6, 2019

"Generic representations of abelian groups and extreme amenability" by J. Melleray and T. Tsankov (Part 1)

Dakota Ihli (UIUC)

Abstract: In this series of talks, we will discuss the paper in the title [arXiv link].

Friday, February 8, 2019

4:00 pm in 345 Altgeld Hall,Friday, February 8, 2019

"The complexity of topological group isomorphism" by A. Kechris, A. Nies, and K. Tent (Part 1)

Anush Tserunyan (UIUC)

Abstract: This will be the introductory talk of the series on the paper in the title [arXiv link], which deals with the classification of some natural classes of non-Archimedean groups (= closed subgroups of S) up to topological group isomorphism. It gives a general criterion for a class of non-Archimedean groups to show that the topological group isomorphism on it is Borel-classifiable by countable structures. This criterion is satisfied by the classes of profinite groups, locally compact non-Archimedean groups, and oligomorphic groups.

Wednesday, February 13, 2019

3:00 pm in 341 Altgeld Hall,Wednesday, February 13, 2019

Introduction to well and even better quasi-orders

Raphaël Carroy (Gödel Research Center for Math. Logic, Univ. of Vienna)

Abstract: Well-quasi-orders, or wqos, generalize well-orders in the context of partial orders. They appear naturally in various domains of mathematics, and have been frequently rediscovered. I'll briefly explain why, and what we can do with them. I'll then talk about their limitations and why it's hard to prove that non-trivial quasi-orders are wqo. I will also show how trying to fix these problems leads to the definition of a smaller class of quasi-orders: better-quasi-orders, or bqos. If time allows, I'll get a bit into bqo theory.

Friday, February 15, 2019

3:00 pm in 341 Altgeld Hall ,Friday, February 15, 2019

Note the time and room change!

"The complexity of topological group isomorphism" by A. Kechris, A. Nies, and K. Tent (Part 2)

Jenna Zomback (UIUC)

Abstract: This will be the second talk of the series on the paper in the title [arXiv link], which deals with the classification of some natural classes of non-Archimedean groups (= closed subgroups of S) up to topological group isomorphism. It gives a general criterion for a class of non-Archimedean groups to show that the topological group isomorphism on it is Borel-classifiable by countable structures. This criterion is satisfied by the classes of profinite groups, locally compact non-Archimedean groups, and oligomorphic groups. In this talk, we will fill in some proofs left out last time and prove this general criterion.

Monday, February 18, 2019

3:00 pm in 341 Altgeld Hall,Monday, February 18, 2019

Dense orbits in the space of subequivalence relations

Forte Shinko (Caltech)

Abstract: Given a measure-preserving countable Borel equivalence relation $E$, there is a Polish space $S(E)$ of subequivalence relations, which admits a natural action of the full group $[E]$. One can ask the following natural question: does $S(E)$ have a dense orbit? We will present results due to François Le Maître which show that the answer is yes when $E$ is the hyperfinite ergodic equivalence relation, and that the answer is no when $E$ is induced by a measure-preserving action of a property (T) group.

Friday, February 22, 2019

4:00 pm in 345 Altgeld Hall ,Friday, February 22, 2019

Cancelled

Friday, March 1, 2019

4:00 pm in 345 Altgeld Hall ,Friday, March 1, 2019

"The complexity of topological group isomorphism" by A. Kechris, A. Nies, and K. Tent (Part 3)

Mary Angelica Gramcko-Tursi (UIUC)

Abstract: This will be the third talk of the series on the paper in the title [arXiv link], which deals with the classification of some natural classes of non-Archimedean groups (= closed subgroups of S) up to topological group isomorphism. It gives a general criterion for a class of non-Archimedean groups to show that the topological group isomorphism on it is Borel-classifiable by countable structures. This criterion is satisfied by the classes of profinite groups, locally compact non-Archimedean groups, and oligomorphic groups. In this talk, we will show that one or two of the aforementioned classes satisfy this criterion.