Department of

Mathematics


Seminar Calendar
for Logic Seminar events the year of Tuesday, February 19, 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.
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Friday, January 18, 2019

4:00 pm in 345 Altgeld Hall,Friday, January 18, 2019

Generic flat pregeometries

Omer Mermelstein (University of Wisconsin, Madison.)

Abstract: The property of "flatness" of a pregeometry (matroid) is best known in model theory as the device with which Hrushovski showed that his example refuting Zilber's conjecture does not interpret an infinite group. I will dedicate the first part of this talk to explaining what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. In the second part, I will conjecture that the family of flat pregeometries associated to strongly minimal sets is model theoretically nice, and share some intermediate results.

Tuesday, January 22, 2019

1:00 pm in Altgeld Hall,Tuesday, January 22, 2019

A Homotopical View of Lascar Groups of First-Order Theories

Greg Cousins (Notre Dame)

Abstract: In this talk, we will discuss how the Lascar group of a first-order theory, $T$, can be recovered as the fundamental group(-oid) of a certain space associated to the category of models, $Mod(T)$. We will then discuss some examples illustrating how tools from algebraic topology can be used to compute the Lascar group of a theory. Time permitting, we will discuss generalizations to the context of AECs and questions their higher homotopy. No knowledge of homotopy theory will be assumed. This is joint work with Tim Campion and Jinhe Ye.

Tuesday, January 29, 2019

1:00 pm in 345 Altgeld Hall,Tuesday, January 29, 2019

Self-similar structures

Garret Ervin (Carnegie Mellon)

Abstract: An iterated function system is a finite collection $f_1, …, f_n$ of contraction mappings on a complete metric space. Every such system determines a unique compact subspace $X$, called the attractor of the system, such that $X = \bigcup f_i[X]$. Many well-known fractals, like the Cantor set and Sierpinski triangle, are realized as attractors of iterated function systems.
 A surprisingly rich analysis can be carried out even when the functions $f_i$ are only assumed to be non-surjective injections from a set to itself. Moreover, in many cases this analysis can be used to characterize when a structure $X$, like a group or linear order, is isomorphic to a product of itself, or to its own square. Such structures behave much like attractors of iterated function systems. We present the technique, and cite solutions to two old problems of Sierpinski as an application.

Tuesday, February 5, 2019

1:00 pm in 345 Altgeld Hall,Tuesday, February 5, 2019

Local Keisler Measures and NIP Formulas

Kyle Gannon (Notre Dame)

Abstract: The connection between finitely additive probability measures and NIP theories was first noticed by Keisler. Around 20 years later, the work of Hrushovski, Peterzil, Pillay, and Simon greatly expanded this connection. Out of this research came the concept of generically stable measures. In the context of NIP theories, these particular measures exhibit stable behavior. In particular, Hrushovski, Pillay, and Simon demonstrated that generically stable measures admit a natural finite approximation. In this talk, we will discuss generically stable measures in the local setting. We will describe connections between these measures and concepts in functional analysis as well as show that this interpretation allows us to derive a local approximation theorem.

Tuesday, February 12, 2019

1:00 pm in 345 Altgeld Hall,Tuesday, February 12, 2019

The Open Graph Dichotomy and the second level of the Borel hierarchy

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

Abstract: I will explain how variants of the open graph dichotomy can be used to obtain various descriptive-set-theoretical dichotomies at the second level of the Borel hierarchy. This shows how to generalise these dichotomies from analytic metric spaces to separable metric spaces by working under the axiom of determinacy. If time allows it, I will also discuss some connections between cardinal invariants and the chromatic number of the graphs at stake.

Tuesday, February 19, 2019

1:00 pm in 345 Altgeld Hall,Tuesday, February 19, 2019

Realizations of countable Borel equivalence relations

Forte Shinko (Caltech)

Abstract: By a classical result of Feldman and Moore, it is known that every countable Borel equivalence relation can be realized as the orbit equivalence relation of a continuous action of a countable group on a Polish space. However, if we impose further conditions, such as requiring the action to be minimal, then it is no longer clear if such a realization exists. We will detail the progress on characterizing when realizations exist under various conditions, including a complete description in the hyperfinite case. This is joint work with Alexander Kechris.

Tuesday, February 26, 2019

1:00 pm in Altgeld Hall,Tuesday, February 26, 2019

n-dependent groups and fields

Nadja Hempel (UCLA)

Abstract: NIP theories are the first class of the hierarchy of n-dependent structures. The random n-hypergraph is the canonical object which is n-dependent but not (n-1)-dependent. Thus the hierarchy is strict. But one might ask if there are any algebraic objects (groups, rings, fields) which are strictly n-dependent for every n? We will start by introducing the n-dependent hierarchy and present all known results on n-dependent groups and fields. These were (more or less) inspired by the above question.

Tuesday, March 5, 2019

1:00 pm in 345 Altgeld Hall,Tuesday, March 5, 2019

Descriptive graph combinatorics with applications to geometry

Spencer Unger (Tel Aviv University)

Abstract: The Banach–Tarski paradox states that (assuming the axiom of choice) a unit ball in $\mathbb{R}^3$ can be partitioned into $5$ sets which can be rearranged by isometries to partition two unit balls. This famous result is part of a larger line of early 20th century research which sought to understand the relation between foundations of measure theory and generalizations of classical ideas such as decomposing polygons into congruent sets.
 In the last few years, there has been a resurgence of interest in these geometrical paradoxes. These results have the unifying theme that the "paradoxical" sets in many classical geometrical paradoxes can surprisingly be much "nicer" than one would naively expect. In this talk, we give a survey of these results and explain a few of the ideas that go in to a constructive solution to Tarski's circle squaring problem. This is joint work with Andrew Marks.

Tuesday, March 12, 2019

1:00 pm in 345 Altgeld Hall,Tuesday, March 12, 2019

Hyperfiniteness and descriptive combinatorics

Clinton Conley (Carnegie Mellon)

Abstract: We survey some recent results on connections between descriptive set-theoretic properties of Borel graphs and hyperfiniteness of their connectedness equivalence relation. For convenience, we will focus on chromatic numbers with various measurability constraints. This talk will include joint work with Jackson, Marks, Miller, Seward, Tucker-Drob.

Tuesday, April 2, 2019

1:00 pm in 345 Altgeld Hall,Tuesday, April 2, 2019

To Be Announced

Ben Hayes (University of Virginia)

Tuesday, April 9, 2019

1:00 pm in 345 Altgeld Hall,Tuesday, April 9, 2019

To Be Announced

Anton Bernshteyn (Carnegie Mellon)

Friday, April 12, 2019

4:00 pm in 345 Altgeld Hall ,Friday, April 12, 2019

To Be Announced

Ward Henson (UIUC)

Tuesday, April 16, 2019

1:00 pm in 345 Altgeld Hall,Tuesday, April 16, 2019

To Be Announced

Levon Haykazyan (University of Waterloo)

Tuesday, April 30, 2019

1:00 pm in 345 Altgeld Hall,Tuesday, April 30, 2019

Dakota Ihli (UIUC)