Tue, 03 May 2022

15:30 - 16:30
Online

Fluctuations of the Characteristic Polynomial of Random Jacobi Matrices

Fanny Augeri
(Weizmann Institute of Science)
Abstract

The characteristic polynomial of a random Hermitian matrix induces naturally a field on the real line. In the case of the Gaussian Unitary ensemble (GUE), this fields is expected to have a very special correlation structure: the logarithm of this field is log-correlated and its maximum is at the heart of a conjecture from Fyodorov and Simm predicting its asymptotic behavior.   As a first step in this direction, we obtained in collaboration with R. Butez and O. Zeitouni, a central limit theorem for the logarithm of the characteristic polynomial of the Gaussian beta Ensembles and for a certain class of random Jacobi matrices. In this talk, I will explain how the tridiagonal representation of the GUE and orthogonal polynomials techniques allow us to analyse the fluctuations of the characteristic polynomial.

Tue, 23 Nov 2021

15:30 - 16:30
L6

Can one hear a real symmetric matrix?

Uzy Smilansky
(Weizmann Institute of Science)
Abstract

The question asked in the title is addressed from two points of view: First, we show that providing enough (term to be explained) spectral data, suffices to reconstruct uniquely generic (term to be explained) matrices. The method is well defined but requires somewhat cumbersome computations. Second, restricting the attention to banded matrices with band-width much smaller than the dimension, one can provide more spectral data than the number of unknown matrix elements. We make use of this redundancy to reconstruct generic banded matrices in a much more straight-forward fashion where the “cumbersome computations” can be skipped over. Explicit criteria for a matrix to be in the non-generic set are provided.

 

Wed, 04 Nov 2020
10:00
Virtual

Is Invariable Generation Hereditary?

Gil Goffer
(Weizmann Institute of Science)
Abstract

I will discuss the notion of invariably generated groups, its importance, and some intuition. I will then present a construction of an invariably generated group that admits an index two subgroup that is not invariably generated. The construction answers questions of Wiegold and of Kantor-Lubotzky-Shalev. This is a joint work with Nir Lazarovich.

Fri, 10 May 2019
13:00
C2

Discrete fundamental group: the large and the small

Federico Vigolo
(Weizmann Institute of Science)
Abstract

The discrete fundamental groups of a metric space can be thought of as fundamental groups that `ignore' closed loops up to some specified size R. As the parameter R grows, these groups have been used to produce interesting invariants of coarse geometry. On the other hand, as R gets smaller one would expect to retrieve the usual fundamental group as a limit. In this talk I will try to briefly illustrate both these aspects.

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