School of Mathematics

Supercuspidal L-packets

Tasho Kaletha
University of Michigan
March 5, 2018
Abstract: Harish-Chandra has given a simple and explicit classification of the discrete series representations of reductive groups over the real numbers. We will describe a very similar classification that holds for a large proportion of the supercuspidal representations of reductive groups over non-archimedean local fields (which we may call regular). The analogy runs deeper: there is a remarkable parallel between the characters of regular supercuspidal representations and the characters of discrete series representations of real reductive groups.

Representations of p-adic groups

Jessica Fintzen
University of Michigan; Member, School of Mathematics
March 5, 2018

Abstract: The building blocks for complex representations of p-adic groups are called supercuspidal representations. I will survey what is known about the construction of supercuspidal representations, mention questions that remain mysterious until today, and explain some recent developments.

Local eigenvalue statistics of random band matrices

Tatyana Shcherbina
Princeton University
February 28, 2018

Random band matrices (RBM) are natural intermediate models to study eigenvalue statistics and quantum propagation in disordered systems, since they interpolate between mean-field type Wigner matrices and random Schrodinger operators. In particular, RBM can be used to model the Anderson metal-insulator phase transition (crossover) even in 1d. In this talk we will discuss some recent progress in application of the supersymmetric method (SUSY) and transfer matrix approach to the analysis of local spectral characteristics of some specific types of RBM.

On the Communication Complexity of Classification Problems

Roi Livni
Princeton University
February 27, 2018

We will discuss a model of distributed learning in the spirit of Yao's communication complexity model. We consider a two-party setting, where each of the players gets a list of labelled examples and they communicate in order to jointly perform a learning task. For example, consider the following problem of Convex Set Disjointness: In this instance Alice and Bob each receive a set of examples in Euclidean space and they need to decide if there exists a hyper-plane that separate the sets.
 

Local to global relations of periods (continued)

Erez Lapid
Weizmann Institute of Science; Member, School of Mathematics
February 27, 2018

Rankin-Selberg integrals provide factorization of certain period integrals into local counterparts. Other, more elusive, periods can be studied in principle by the relative trace formula and other methods.
 
Following Waldspurger, Ichino-Ikeda formulated a local to global conjecture about the Gross-Prasad periods. A more general setup was subsequently considered by Sakellaridis-Venkatesh.
 
I will discuss some of these principles as well as a result on Whittaker coefficients joint with Zhengyu Mao.

Representations of p-adic groups

Jessica Fintzen
University of Michigan
February 26, 2018

I will survey what is known about the construction of (the building blocks of) representations of p-adic groups, mention recent developments, and explain some of the concepts underlying all constructions. In particular, I will introduce filtrations of p-adic groups and indicate some of their remarkable properties.

A Tight Bound for Hypergraph Regularity

Guy Moshkovitz
Harvard University
February 26, 2018

The hypergraph regularity lemma — the extension of Szemeredi's graph regularity lemma to the setting of k-graphs — is one of the most celebrated combinatorial results obtained in the past decade. By now there are various (very different) proofs of this lemma, obtained by Gowers, Rodl et al. and Tao. Unfortunately, what all these proofs have in common is that they yield partitions whose order is given by the k-th Ackermann function.