Seminar Calendar
for Descriptive Set Theory events the next 12 months of Sunday, January 1, 2017.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, January 27, 2017

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, January 27, 2017
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Submitted by anush.
Anush Tserunyan (UIUC Math)
On "Structurable equivalence relations" by R. Chen and A. Kechris: Introduction
Abstract: For a class $\mathcal{K}$ of countable relational structures, a countable Borel equivalence relation $E$ is said to be $\mathcal{K}$-structurable if there is a Borel way to put a structure from $\mathcal{K}$ on each $E$-equivalence class. The paper of Chen and Kechris [arXiv link] studies the global structure (including Borel homomorphisms and reductions) of the classes of $\mathcal{K}$-structurable equivalence relations for various $\mathcal{K}$. In this introductory talk, we will give some background and survey the main results of the paper.

Friday, February 3, 2017

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, February 3, 2017
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Submitted by anush.
Anush Tserunyan (UIUC Math)
On "Structurable equivalence relations" by R. Chen and A. Kechris: Universal equivalence relations (2nd talk)
Abstract: In our previous talk, we stated the first main result of the paper: a characterization of the elementary classes of countable equivalence relations. In this second talk, we prove that every elementary class admits a $\sqsubseteq_B^i$-universal equivalence relation. This implies one direction of the aforementioned characterization.

Friday, February 10, 2017

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, February 10, 2017
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Submitted by anush.
Anush Tserunyan (UIUC Math)
On "Structurable equivalence relations" by R. Chen and A. Kechris: Characterization of elementary classes (3rd talk)
Abstract: In our previous talk, we proved that any elementary class of equivalence relations admits an invariantly injective universal element. This completes one direction of the characterization of elementary classes. In this third talk, we will prove the other direction of the characterization, as well as discuss other results of the paper if time permits.

Friday, February 17, 2017

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, February 17, 2017
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Submitted by anush.
Erik Walsberg (UIUC Math)
"Strong theories of ordered abelian groups" by A. Dolich and J. Goodrick: Introduction

Friday, February 24, 2017

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, February 24, 2017
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Submitted by anush.
Aristotelis Panagiotopoulos (UIUC Math)
On "Structurable equivalence relations" by R. Chen and A. Kechris: Structurability by structures with TDC (4th talk)
Abstract: In this talk, we prove a theorem of A. Marks included in the current paper. It says that every aperiodic countable Borel equivalence relation can be $\mathcal{A}$-structured for any countable structure $\mathcal{A}$ with trivial definable closure (TDC). Examples include the rationals, the random graph, and the rational Urysohn sphere.

Friday, March 10, 2017

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, March 10, 2017
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Submitted by erikw.
Travis Nell (UIUC Math)
Strong Theories of Ordered Abelian groups
Abstract: We will continue discussing the paper "Strong Theories of Ordered Abelian Groups" by A. Dolich and J. Goodrick

Thursday, April 6, 2017

Descriptive Set Theory Seminar
1:00 pm   in 7 Illini Hall,  Thursday, April 6, 2017
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Submitted by anush.
Anton Bernshteyn (UIUC Math)
Baire measurable colorings of group actions
Abstract: Suppose that a countable group $\Gamma$ acts continuously on a Polish space $X$ and denote this action by $\alpha$. Does there exist a Baire measurable coloring $f \colon X \to \mathbb{N}$ satisfying certain local constraints? Or, better to say, can we characterize the coloring problems which admit Baire measurable solutions over $\alpha$? We will show that, on the one hand, there is no such Borel characterization—the problem is complete analytic. On the other hand, when $\alpha$ is the shift action, we prove that, roughly speaking, a Baire measurable coloring exists if and only if it can be found by a greedy algorithm.

Friday, April 7, 2017

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 245 Altgeld Hall,  Friday, April 7, 2017
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Submitted by erikw.
Lou van den Dries (UIUC)
Model Theory as a Geography of Mathematics
Abstract: This is a dry run for the first talk in the Tarski lectures I am giving the week after in Berkeley. This first talk is for a rather general audience of mathematicians, logicians, and philosophers. I like to think of model theory as a {\em geography of mathematics \}, especially of its ``tame'' side. Here {\em tame\/} roughly corresponds to {\em geometric\/} as opposed to {\em combinatorial-arithmetic}. In this connection I will discuss Tarski's work on the real field, and the notion of o-minimality that it suggested. A structure $M$ carries its own mathematical territory with it, via interpretability: its own posets, groups, fields,and so on. Understanding this ``world according to $M$'' can be rewarding. Stability-like properties of $M$ forbid certain combinatorial patterns, thus providing highly intrinsic and robust information about this world.

Friday, April 14, 2017

Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, April 14, 2017
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Submitted by anush.
Anton Bernshteyn (UIUC Math)
Baire measurable colorings of group actions: Part Ⅱ
Abstract: Suppose that a countable group $\Gamma$ acts continuously on a Polish space $X$ and denote this action by $\alpha$. Does there exist a Baire measurable coloring $f \colon X \to \mathbb{N}$ satisfying certain local constraints? Or, better to say, can we characterize the coloring problems which admit Baire measurable solutions over $\alpha$? We will show that, on the one hand, there is no such Borel characterization—the problem is complete analytic. On the other hand, when $\alpha$ is the shift action, we prove that, roughly speaking, a Baire measurable coloring exists if and only if it can be found by a greedy algorithm.

Friday, April 21, 2017

Descriptive Set Theory Seminar
2:00 pm   in 243 Altgeld Hall,  Friday, April 21, 2017
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Submitted by anush.
Anton Bernshteyn (UIUC Math)
Baire measurable colorings of group actions: Part Ⅲ
Abstract: Suppose that a countable group $\Gamma$ acts continuously on a Polish space $X$ and denote this action by $\alpha$. Does there exist a Baire measurable coloring $f \colon X \to \mathbb{N}$ satisfying certain local constraints? Or, better to say, can we characterize the coloring problems which admit Baire measurable solutions over $\alpha$? We will show that, on the one hand, there is no such Borel characterization—the problem is complete analytic. On the other hand, when $\alpha$ is the shift action, we prove that, roughly speaking, a Baire measurable coloring exists if and only if it can be found by a greedy algorithm.

Friday, April 28, 2017

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, April 28, 2017
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Submitted by ssolecki.
Ward Henson (UIUC, UC Berkeley)
On definability and interpretability in model theory
Abstract: This will be an expository talk. Topics covered/mentioned will include: extension by definition and expansion/extension by interpretation (the eq-construction), Beth's Theorem (characterizing definability), and Makkai's Theorem (characterizing the eq-expansion). The setting will be model theory of classical (discrete) structures and then of metric (real-valued) structures. In the metric setting, definability of sets/relations has some subtleties that do not arise in discrete structures.

Thursday, May 11, 2017

Graduate Analysis Seminar
3:00 pm   in 243 Altgeld,  Thursday, May 11, 2017
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Submitted by compaan2.
Aristotelis Panagiotopoulos   [email] (UIUC Math)
The Complexity of Classifying Unitaries
Abstract: Classification problems occur in all areas of mathematics. Descriptive set theory provides methods for measuring the complexity of such problems. For example, using a technique developed by Hjorth, Kechris and Sofronidis proved that the problem of classifying all unitary operators of an infinite dimensional Hilbert space up to unitary equivalence is strictly more difficult than classifying graph structures on domain N up to isomorphism. In this talk I will review the basics from descriptive set theory and explain why the problem of classifying unitaries is so hard. Part of my talk will be based on recent joint work with Martino Lupini.