Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, April 11, 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, April 11, 2019

11:00 am in 241 Altgeld Hall,Thursday, April 11, 2019

#### Vanishing of Hyperelliptic L-functions at the Central Point

###### Wanlin Li (Wisconsin Math)

Abstract: We study the number of quadratic Dirichlet L-functions over the rational function field which vanish at the central point s=1/2. In the first half of my talk, I will give a lower bound on the number of such characters through a geometric interpretation. This is in contrast with the situation over the rational numbers, where a conjecture of Chowla predicts there should be no such L-functions. In the second half of the talk, I will discuss joint work with Ellenberg and Shusterman proving as the size of the constant field grows to infinity, the set of L-functions vanishing at the central point has 0 density.

12:30 pm in 464 Loomis,Thursday, April 11, 2019

#### Effective field theory and effective response away from equilibrium

###### Paolo Glorioso (University of Chicago)

Abstract: In the first part of this talk I will describe how the formalism of non-equilibrium effective field theory (EFT) provides a field-theoretical description of the low-energy behavior of systems in local thermal equilibrium. I will then show how magnetohydrodynamics can be incorporated in this formalism using generalized global symmetries. In the second part of the talk I will discuss response for Floquet systems, which do not possess a notion of equilibrium, and for which we lack of an effective theory formulation. I will show how this can be remedied by applying the approach of non-equilibrium EFT to describe topological response of such systems.

2:00 pm in 241 Altgeld Hall,Thursday, April 11, 2019

#### Conversations on the exceptional character

Abstract: We will spend the last few weeks of the semester discussing Landau-Siegel zeros. In particular, we will be discussing Henryk Iwaniec's survey article "Conversations on the exceptional character."

2:00 pm in 347 Altgeld Hall,Thursday, April 11, 2019

#### Local Limit Theorem

###### Qiang Wu (UIUC Math)

Abstract: This talk is an introduction to some classical CLT variants, specifically on local limit theorem (LLT). The proof of classical LLT for lattice and non-lattice distribution will be discussed using the characteristic approach. Other various generalizations of LLT will be pointed out. Finally, a concise combinatorial approach for LLT of simple random walk will be sketched. Time permits, I will talk about the generalized Berry-Esseen Inequality.

4:00 pm in 245 Altgeld Hall,Thursday, April 11, 2019

#### Recent progress on existence of minimal surfaces

###### André Neves (University of Chicago)

Abstract: A long standing problem in geometry, conjectured by Yau in 1982, is that any any $3$-manifold admits an infinite number of distinct minimal surfaces. The analogous problem for geodesics on surfaces led to the discovery of deep interactions between dynamics, topology, and analysis. The last couple of years brought dramatic developments to Yau’s conjecture, which has now been settled due to the work of Marques-Neves and Song. In the first talk I will survey the history of the problem and the several contributions made. In the second talk I will talk about the Weyl law for the volume spectrum (Marques-Neves-Liokumovich) and how it can be used to prove denseness and equidistribution of minimal surfaces in the generic case (Irie-Marques-Neves and Marques-Neves-Song). In the third talk I will survey the recent breakthroughs due to Song, Zhou, and Mantoulidis-Chodosh.

Bio Note: André Neves is a leading figure in geometric analysis with important contributions ranging from the Yamabe problem to geometric flows. Jointly with Fernando Marques, he transformed the field by introducing new ideas and techniques that led to the solution of several open problems which were previously out of reach. Together or with coauthors, they solved the Willmore conjecture, the Freedman-He-Wang conjecture in knot theory and Yau’s conjecture on the existence of minimal surfaces in the generic case.

Neves received his PhD from Stanford University in 2005 under the supervision of Richard Schoen. He was a postdoctoral fellow and assistant professor at Princeton University, before joining the Imperial College of London in 2011, where he became a full professor. He joined the faculty of the University of Chicago in 2016. Among his many awards and recognitions, Neves was awarded the Philip Leverhulme Prize in 2012, the LMS Whitehead Prize in 2013, he was invited speaker at ICM in Seoul in 2014, received a New Horizons in Mathematics Prize in 2015, and the 2016 Oswald Veblen Prize in Geometry. In 2018, he received a Simons Investigator Award.

5:00 pm in TBA,Thursday, April 11, 2019