Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, September 13, 2018.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, September 13, 2018

11:00 am in 241 Altgeld Hall,Thursday, September 13, 2018

#### Breaking the 1/2-barrier for the twisted second moment of Dirichlet L-functions

###### Kyle Pratt (University of Illinois)

Abstract: Our seminar lecture on Thursday will be given by Kyle Pratt. His title and abstract are given below. Title: Breaking the 1/2-barrier for the twisted second moment of Dirichlet L-functions Abstract: I will discuss very recent work, joint with Bui, Robles, and Zaharescu, on a moment problem for Dirichlet L-functions. The talk will be accessible, as I will give lots of background information and will not dwell on technicalities.

2:00 pm in 241 Altgeld,Thursday, September 13, 2018

#### The Combinatorics of Second Order Mock Theta Functions

###### Hannah Burson (University of Illinois at Urbana-Champaign)

Abstract: Less than a year before his death, Ramanujan wrote a letter to Hardy introducing mock theta functions and listing 17 examples of such functions. Zwegers' 2002 thesis allowed for the discovery of infinite families of mock theta functions. The second order mock theta functions are an example of more recently discovered mock theta functions. This talk will introduce new combinatorial interpretations of a general second-order mock theta function identity. In the process, we will talk about some famous results in the theory of partitions and some of the history of Ramanujan.

2:00 pm in 243 Altgeld Hall,Thursday, September 13, 2018

#### Some results for the Chevyshev Greedy Algorithm

###### Eugenio Hernández (Universidad Autónoma de Madrid)

Abstract: I will present some estimates for the Lebesgue type parameter of the Chevyshev Greedy Algorithm as well as for the weak thresholding variant. Some examples will be presented showing the optimality of the results.

3:00 pm in 345 Altgeld Hall,Thursday, September 13, 2018

#### On modular functors and representation theory

###### Alexander Shapiro   [email] (Edinburgh)

Abstract: A quantized higher Teichmüller theory assigns an algebra and its Hilbert space representation to each choice of a surface and a Lie group G. The modular functor conjecture, as formulated by Fock and Goncharov, predicts how this assignment behaves under cutting and gluing of surfaces. I will outline a proof of this conjecture for G=SL_n and discuss how different statements on positive representations of quantum groups arise as particular cases of the conjecture. This is a joint work with Gus Schrader.

4:00 pm in 245 Altgeld Hall,Thursday, September 13, 2018

#### Model theory and ultraproducts

###### Maryanthe Malliaris (University of Chicago)

Abstract: The ultraproduct construction gives a way of averaging an infinite sequence of mathematical structures, such as fields, graphs, or linear orders. The talk will be about the strength of such a construction.