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Seminar Calendar
for events the day of Thursday, April 13, 2017.

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Thursday, April 13, 2017

11:00 am in 241 Altgeld Hall,Thursday, April 13, 2017

Limits of function field Bernoulli-Carlitz numbers

Matt Papanikolas (Texas A&M University)

Abstract: Because of the classical Kummer congruences, one is able to take p-adic limits of certain natural subsequences of Bernoulli numbers. This leads to notions of p-adic limits of special zeta values and Eisenstein series. In the case of the rational function field K over a finite field, the analogous quantities, called Bernoulli-Carlitz numbers, fail to satisfy Kummer-type congruences. Nevertheless, we prove that certain subsequences of Bernoulli-Carlitz numbers do have v-adic limits, for v a finite place of K, thus leading to new v-adic limits of Eisenstein series. Joint with G. Zeng.

12:00 pm in 243 Altgeld Hall,Thursday, April 13, 2017

Stable Strata of Geodesics in Outer Space

Catherine Pfaff (UC Santa Barbara)

Abstract: Outer automorphisms of free groups are understood via their action on Culler-Vogtmann Outer space. We study the behavior of geodesics in Outer Space by focusing on a class of geodesics that have strong stability properties. We further show that pathologies exist among these geodesics that don't occur, for example, in the Teichmuller space setting. This is joint work with Yael Algom-Kfir and Ilya Kapovich.

12:30 pm in 464 Loomis Laboratory,Thursday, April 13, 2017

Toward classification of 5d SQFTs

Hee-Cheol Kim (Harvard Physics)

Abstract: Non-trivial 5d SUSY theories can be engineered in string theory by using brane constructions or M-theory compactification on CY3. Such theories have interacting UV fixed points. We propose a systematic way to classify non-trivial 5d gauge theories by extending the previous attempt by Intriligator, Morrison and Seiberg. We will present the full classification of 5d gauge theories with simple gauge groups which flow to non-trivial fixed points.

2:00 pm in 241 Altgeld Hall,Thursday, April 13, 2017

L-values, Bessel moments and Mahler measures

Detchat Samart   [email] (UIUC)

Abstract: We will discuss some formulas and conjectures relating special values of L-functions associated to modular forms to moments of Bessel functions and Mahler measures. Bessel moments arise in the study of Feynman integrals, while Mahler measures have received a lot of attention from mathematicians over the past few decades due to their apparent connection with number theory, algebraic geometry, and algebraic K-theory. Though easy to verify numerically with high precision, most of these formulas turn out to be ridiculously hard to prove, and no machinery working in full generality is currently known. Some available techniques which have been used to tackle these problems will be demonstrated. Time permitting, we will present a meta conjecture of Konstevich and Zagier which gives a general framework of how one could verify these formulas using only elementary calculus.

2:00 pm in 243 Altgeld Hall,Thursday, April 13, 2017

Metric characterization of the Radon-Nikodým property in Banach spaces

Mikhail Ostrovskii (St. John's University)

Abstract: The Radon-Nikodým property (RNP) can be characterized in many different analytic, geometric, and probabilistic ways. The RNP plays an important role in the theory of metric embeddings (works of Cheeger, Kleiner, Lee, and Naor (2006-2009)). In this connection Johnson (2009) suggested the problem of metric characterization of the RNP. The main goal of the talk is to explain the speaker's solution of this problem in terms of thick families of geodesics.

3:00 pm in 347 Altgeld Hall,Thursday, April 13, 2017

A crystal structure on shifted tableaux, with applications to type B Schubert curves

Maria Gillespie (UC Davis)

Abstract: We present a new crystal-like structure on shifted (marked) semistandard skew tableaux. The raising and lowering operators commute with jeu de taquin slides, and detect the type B Littlewood-Richardson condition as the highest weight entries. Certain substructures satisfy the Kashiwara crystal axioms for the root system of $\mathrm{GL}_n$. If time permits, we will discuss applications of our new operators to Schubert curves in the orthogonal Grassmannian. This is joint work with Jake Levinson and Kevin Purbhoo.

4:00 pm in 245 Altgeld Hall,Thursday, April 13, 2017

Spring Department Faculty Meeting

Abstract: The Spring Department Faculty Meeting will be held at 4 p.m. in 245 Altgeld Hall, followed by a reception in 239 Altgeld Hall.