Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, January 23, 2018.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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1  2       1  2  3  4  5  6                1  2  3
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Tuesday, January 23, 2018

12:00 pm in 243 Altgeld Hall,Tuesday, January 23, 2018

#### A Garden of Eden Theorem for Abelian Harmonic Models

###### Tullio Ceccherini-Silberstein (University of Sannio)

Abstract: In this talk, completely self contained (I'll recall the basic of Pontryagin duality), I would like to introduce the audience to the beautiful theory of algebraic actions (in the sense of K. Schmidt) and present a Garden of Edent type theorem for the class of weakly-expansive principal algebraic actions of Abelina groups, which includes, as a particular case, transient Abelian Harmonic Models. This is a recent result obtained in collaboration with Michel Coornaert and Hanfeng Li.

1:00 pm in 345 Altgeld Hall,Tuesday, January 23, 2018

#### First order expansions of the ordered real additive group

###### Erik Walsberg (UIUC Math)

Abstract: I will discuss joint work with Philipp Hieronymi on first order expansions of $(\mathbb{R},<,+)$. The definable subsets of $\mathbb{R}^n$ in the known natural model-theoretically tame expansions are geometrically tame objects. Many of these examples satisfy the essentially strongest geometric tameness assumption, o-minimality. In this talk I will discuss type A expansions. The assumption of being type A appears to be the broadest possible generalization of o-minimality for expansions of $(\mathbb{R},<,+)$ as some of the main o-minimal tools extend to this setting, and do not appear to extend further.

2:00 pm in 347 Altgeld Hall,Tuesday, January 23, 2018

#### Effective Analytic Combinatorics in Several Variables

###### Steve Melczer (U. Penn.)

Abstract: The field of analytic combinatorics studies the asymptotic behaviour of sequences through analytic properties of their generating functions. In addition to the now classical univariate theory, recent work in the study of analytic combinatorics in several variables (ACSV) has shown how to derive asymptotics for the coefficients of certain D-finite functions by representing them as diagonals of multivariate rational functions. We detail the rich theory of ACSV from a computer algebra viewpoint, with an eye towards automatic implementations that can be used by those with no specialized knowledge in the field. Applications from several areas of combinatorics, number theory, and physics will be discussed.

3:00 pm in 241 Altgeld Hall,Tuesday, January 23, 2018

#### Topological version of Pach's overlap theorem

###### Boris Bukh (Carnegie Mellon Math)

Abstract: Given a large point set in the plane, where is its 'center'? Unlike the 1-dimensional case, there is not a single answer. We will discuss some of these answers, with the focus on the result of Pach. He showed that one can always find three large subsets A,B,C and a 'central point' p such that every A-B-C triangle contains p. We will then explain the topological generalization of this and related results, where for example the triangle edges are no longer assumed to be straight. Based on a joint work with Alfredo Hubard.

4:00 pm in Illini Hall 1,Tuesday, January 23, 2018

#### Moduli space of compact Riemann surfaces

###### Jin Hyung To (UIUC)

Abstract: We will overview the moduli space of compact Riemann surfaces.

5:00 pm in 314 Altgeld Hall,Tuesday, January 23, 2018

#### IGL Kickoff Meeting

Abstract: Spring 2018 organizational meeting for the Illinois Geometry Lab.