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

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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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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

Tuesday, March 14, 2017

Logic Seminar
1:00 pm   in Altgeld Hall,  Tuesday, March 14, 2017
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Submitted by erikw.
James Freitag (UIC Math)
Model theory and Painleve equations
Abstract: We will discuss how to use model theory to prove some transcendence results for solutions of Painleve equations.

Tuesday, April 4, 2017

Logic Seminar
1:00 pm   in UIC SEO 636,  Tuesday, April 4, 2017
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Submitted by phierony.
MidWest Model Theory Day at UIC
Abstract: see http://homepages.math.uic.edu/~freitag/MWMT11

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.

Wednesday, April 12, 2017

Doob Colloquium
3:00 pm   in 243 Altgeld Hall,  Wednesday, April 12, 2017
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Submitted by lescobar.
Erik Walsberg (UIUC)
First order logic and Sub-riemannian spheres.
Abstract: I will discuss a connection between sub-riemannian geometry and first order model theory. Researchers in sub-riemannian geometry have essentially been working on the following: are sub-riemannian spheres definable in an o-minimal expansion of the ordered field of real numbers? (O-minimality is an important and popular topic in model theory developed in large part by UIUC's own Lou van den Dries). It also seems that some model theorists have been trying to construct the kind of structure that the geometers are looking for. As far as I can tell neither side was really aware of what the other was doing until now. I will try to explain some of this. No knowledge of logic or sub-riemannian geometry is necessary.

Friday, April 21, 2017

Model Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, April 21, 2017
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Submitted by erikw.
Matthias Aschenbrenner (UCLA)
The logical complexity of finitely generated commutative rings
Abstract: Since the work of G\"odel we know that the theory of the ring $\mathbb Z$ of integers is very complicated. Using the coding techniques introduced by him, every finitely generated commutative ring can be interpreted in $\mathbb Z$ and therefore has a theory which is no more complicated than that of $\mathbb Z$. It has also been long known that conversely, every infinite finitely generated commutative ring interprets the integers, and hence its theory is at least as complex as that of $\mathbb Z$. However, this mutual interpretability does not fully describe the class of definable sets in such rings. The correct point of view is provided by the concept of bi-interpretability, an equivalence relation on the class of first-order structures which captures what it means for two structures to essentially have the same categories of definable sets and maps. We characterize algebraically those finitely generated rings which are bi-interpretable with $\mathbb Z$. (Joint work with Anatole Kh\'elif, Eudes Naziazeno, and Thomas Scanlon.)

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.