Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, December 12, 2019.

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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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Thursday, December 12, 2019

2:00 pm in 239 Altgeld Hall,Thursday, December 12, 2019

#### IGL Fall 2019 Open hpouse

Abstract: The IGL Open house will take place on Reading Day December 12 2-5pm in 239 Altgeld Hall.Undergraduate students who participated in IGL project in the Fall semester will present posters with their research findings.

3:00 pm in 347 Altgeld Hall,Thursday, December 12, 2019

#### Divided symmetrization, Schubert polynomials and quasisymmetric functions

###### Vasu Tewari   [email] (University of Pennsylvania)

Abstract: The procedure of divided symmetrization was introduced by Alex Postnikov in the context of computing volume polynomials of various classes of permutahedra. This procedure takes a multivariate polynomial as input and outputs a scalar, which in many cases is a combinatorially interesting quantity. In this talk, I will describe how performing divided symmetrization is equivalent to reducing multivariate polynomials modulo the ideal generated by the homogeneous quasi-symmetric polynomials of positive degree in a fixed number of variables. I will subsequently discuss how divided symmetrization can be used to understand the Schubert expansion of the Anderson-Tymoczko class of the Peterson variety. Along the way, we will encounter familiar combinatorial objects such as flagged tableaux, reduced pipe dreams, P-partitions and various Catalan objects. This is joint work with Philippe Nadeau at Institut Camille Jordan.

4:00 pm in 245 Altgeld Hall,Thursday, December 12, 2019

#### Combinatorics and Descriptive Set Theory in Banach Spaces

###### Pavlos Motakis   [email] (Illinois Math)

Abstract: Surprising as it may sound, these a-priori unrelated topics have had an immense impact on the study of geometric properties of Banach spaces. Ramsey Theory, a branch of Combinatorics, has far reaching implications to studying symmetries in Banach spaces, their asymptotic properties, and properties of bounded linear operators. The study of reasonably defined sets, which is the topic of Descriptive Set Theory, is an effective tool for answering universality problems in Banach spaces and measuring the complexity of classes of them.