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for events the day of Tuesday, February 4, 2020.

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Tuesday, February 4, 2020

12:00 pm in 243 Altgeld Hall,Tuesday, February 4, 2020

Sofic groups, sofic entropy and surjunctivity of dynamical systems

Tullio Ceccherini-Silberstein (Università degli Studi del Sannio)

Abstract: A dynamical system is a pair $(X, G)$ where $X$ is a compact metrizable space and $G$ is a countable group acting on $X$ by homeomorphisms. An endomorphism of $(X, G)$ is a continuous map from $X$ to $X$ which commutes with the action of $G$. A dynamical system is surjunctive if every injective endomorphism is surjunctive, and therefore a homeomorphism. Sofic groups were introduced by Gromov and Weiss as a generalization of both residually finite groups and amenable groups. A celebrated theorem of Gromov (and Weiss) is that if $A$ is a finite set and $G$ is sofic, then $(AG, G)$ is surjunctive. In recent work with Michel Coornaert and Hanfeng Li we generalize the Gromov-Weiss theorem to show that every dynamical system $(X, G)$ with certain suitable properties is surjunctive.

1:00 pm in Altgeld Hall,Tuesday, February 4, 2020

To Be Announced

1:00 pm in 241 Altgeld Hall,Tuesday, February 4, 2020

Model-theoretic techniques in query learning

Hunter Chase (UIC)

Abstract: Several notions of complexity of set systems correspond both with model-theoretic dividing lines and notions of machine learning. We describe a new connection between query learning and stable formulas without the finite cover property.

1:00 pm in 347 Altgeld Hall,Tuesday, February 4, 2020

Local smoothing estimates for Fourier Integral Operators

David Beltran (U. Wisconsin, Madison)

Abstract: The sharp fixed-time Sobolev estimates for Fourier Integral Operators (and therefore solutions to wave equations in Euclidean space or compact manifolds) were established by Seeger, Sogge and Stein in the early 90s. Shortly after, Sogge observed that a local average in time leads to a regularity improvement with respect to the sharp fixed-time estimates. Establishing variable-coefficient counterparts of the Bourgain—Demeter decoupling inequalities, we improve the previous best known local smoothing estimates for FIOs. Moreover, we show that our results are sharp in both the Lebesgue and regularity exponent (up to the endpoint) in odd dimensions. This is joint work with Jonathan Hickman and Christopher D. Sogge.

2:00 pm in 243 Altgeld Hall,Tuesday, February 4, 2020

The Game of Plates and Olives

Sean English (University of Illinois, Urbana-Champaign)

Abstract: Much can be learned about a manifold by studying the smooth functions on it. One particularly nice type of functions are Morse Functions. The game of plates and olives was formulated by Nicolaescu to study an enumeration problem related to Morse functions on the 2-sphere.

In the game of plates and olives, there are four different types of moves:
1.) add a new plate to the table,
2.) combine two plates and their olives onto one plate, removing the second plate from the table,
3.) add an olive to a plate, and
4.) remove an olive from a plate.

We will look at the original problem of enumerating Morse functions on the sphere, and also will look at the game of plates and olives when it is played by choosing a move to make at each step randomly. We will see that with high probability the number of olives grows linearly as the total number of moves goes to infinity.

This project was joint work with Andrzej Dudek and Alan Frieze.

3:00 pm in 243 Altgeld Hall,Tuesday, February 4, 2020

Moduli spaces of Lagrangians in symplectic topology and mirror symmetry

James Pascaleff (UIUC)

Abstract: Moduli spaces of Lagrangians (as objects in Fukaya categories), and the geometry on such moduli spaces, may be used to understand problems in symplectic topology and mirror symmetry. In this talk, I will introduce these ideas and give an example showing how to use symplectic topology to solve a problem about Laurent polynomials (based on joint work with Dmitry Tonkonog).