Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, October 31, 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, October 31, 2019

11:00 am in 241 Altgeld Hall,Thursday, October 31, 2019

#### Eisenstein ideal with squarefree level

###### Carl Wang-Erickson (University of Pittsburgh)

Abstract: In his landmark paper "Modular forms and the Eisenstein ideal," Mazur studied congruences modulo a prime p between the Hecke eigenvalues of an Eisenstein series and the Hecke eigenvalues of cusp forms, assuming these modular forms have weight 2 and prime level N. He asked about generalizations to squarefree levels N. I will present some work on such generalizations, which is joint with Preston Wake and Catherine Hsu.

12:00 pm in 243 Altgeld Hall,Thursday, October 31, 2019

#### Monopole Floer homology and spectral geometry of hyperbolic three-manifolds

###### Francesco Lin (Columbia University)

Abstract: By studying the Seiberg-Witten equations, Kronheimer and Mrowka defined a package of invariants of three-manifolds called monopole Floer homology. In this talk, we discuss some interactions between this topological invariant and the spectral geometry of the Laplacian on the underlying Riemannian manifold, with the goal of understanding concrete examples of hyperbolic manifolds. This is joint work with Mike Lipnowski.

1:00 pm in 464 Loomis Laboratory,Thursday, October 31, 2019

#### Multitrace excited states and perturbative entropy divergences

###### Antony Speranza (Perimeter Institute)

Abstract: Perturbative calculations of entanglement entropy have found a number of recent applications in understanding field theory, holography, and quantum gravity. In this talk, I will discuss a class of excited states of a CFT formed from a Euclidean path integral with nonlocal multitrace insertions, with an eye toward understanding their entanglement structure holographically. Such states are argued to have good semiclassical holographic duals, but can possess nontrivial bulk entanglement structure at order N^0. A surprising feature of these states is that divergences occur quite generically in the perturbative expansion of their entanglement entropy. These divergences signal a nonanalyticity in the expansion, and must be resummed in computing the full expression for the entropy. This resummation is challenging in general, but I will describe some simplified examples in which it may be tractable. In the process, I will also give some general techniques for diagnosing when such nonanalyticities occur, and point to some indications that they may in general be calculable. This talk is based on arXiv:1904.01584 and ongoing work.

2:00 pm in 243 Altgeld Hall,Thursday, October 31, 2019

#### Matrix Convex Sets, Tensor Products, and Noncommutative Choquet Boundaries

###### Roy Araiza (Purdue )

Abstract: I will discuss tensor products in the category of matrix convex sets and discuss how we may relate the study of their Choquet theory to questions about tensor product nuclearity. Based on joint work with Adam Dor-On and Thomas Sinclair.

3:00 pm in 347 Altgeld Hall,Thursday, October 31, 2019

#### The combinatorics of spherical Schubert varieties

###### Reuven Hodges   [email] (University of Illinois at Urbana-Champaign )

Abstract: Over the last several years, in joint work with V. Lakshmibai and M. B. Can, I have been studying Levi subgroup actions on Schubert varieties. I plan to discuss some of the combinatorial questions that have arisen from this work. I will introduce skew Schur functions and their decomposition in the basis of Schur functions, as well as when these decompositions are multiplicity free. Then we will discuss several problems involving these multiplicities. To conclude, I will illustrate how the answer to these multiplicity problems allows us to classify all Schubert varieties in the Grassmannian and Levi subgroups such that the Levi acts spherically on the Schubert variety.