2019 Apr 10

# Analysis Seminar: Gregory Berkolaiko (Texas A&M) "Nodal statistics of graph eigenfunctions"

12:00pm to 1:00pm

## Location:

Ross 70
Title: Nodal statistics of graph eigenfunctions
Abstract: Understanding statistical properties of zeros of Laplacian
eigenfunctions is a program which is attracting much attention from
mathematicians and physicists. We will discuss this program in the
setting of "quantum graphs", self-adjoint differential operators
acting on functions living on a metric graph.
Numerical studies of quantum graphs motivated a conjecture that the
distribution of nodal surplus (a suitably rescaled number of zeros of
2019 Mar 27

# Analysis Seminar: Ofer Zeitouni (Weizmann) "Perturbations of non-normal matrices"

12:00pm to 1:00pm

## Location:

Ross 70
Title: Perturbations of non-normal matrices
Abstract: Eigenvalues of Hermitian matrices are stable under perturbations in the sense that the $l_p$ norm of the difference between (ordered)eigenvalues is bounded by the Schatten norm of the perturbation. A similar control does not hold for non-Normal matrices. In the talk, I will discuss
2018 Nov 13

# Dynamics Lunch: Jakub Konieczny "Sarnak conjecture and automatic sequences (following C. Müllner and M. Lemańczyk)"

12:00pm to 1:00pm

## Location:

Manchester faculty club
2018 Dec 04

# Dynamics Seminar: Omri Sarig (Weizmann) Local limit theorems for inhomogeneous Markov chains

2:15pm to 3:15pm

Abstract: An inhomogeneous Markov chain X_n is a Markov chain whose state spaces and transition kernels change in time. A “local limit theorem” is an asymptotic formula for probabilities of th form
Prob[S_N-z_N\in (a,b)] , S_N=f_1(X_1,X_2)+....+f_N(X_N,X_{N+1})
in the limit N—>infinity. Here z_N is a “suitable” sequence of numbers.
I will describe general sufficient conditions for such results.
If time allows, I will explain why such results are needed for the study of certain problems related to irrational rotations.
2018 Oct 23

# Dynamics Seminar: Nishant Chandgotia (HUJI). Some universal models for Z^d actions

2:15pm to 3:15pm

## Location:

Ross 70

Krieger’s generator theorem shows that any free invertible ergodic measure preserving action (Y,\mu, S) can be modelled by A^Z (equipped with the shift action) provided the natural entropy constraint is satisfied; we call such systems (here it is A^Z) universal. Along with Tom Meyerovitch, we establish general specification like conditions under which Z^d-dynamical systems are universal. These conditions are general enough to prove that
1) A self-homeomorphism with almost weak specification on a compact metric space (answering a question by Quas and Soo)
2018 Nov 20

2:15pm to 3:15pm

2018 Nov 13

2:15pm to 3:15pm

Ross 70

2018 Dec 05

# Analysis Seminar: Ron Rosenthal (Technion) "Eigenvector correlation in the complex Ginibre ensemble"

12:00pm to 1:00pm

Title: Eigenvector correlation in the complex Ginibre ensemble
Abstract:
The complex Ginibre ensemble is a non-Hermitian random matrix on $\mathbb{C}^N$ with i.i.d. complex Gaussian entries normalized to have mean zero and variance $1/N$. Unlike the Gaussian unitary ensemble, for which the eigenvectors are orthogonal, the geometry
of the eigenbases of the Ginibre ensemble are not particularly well understood.
2018 Dec 11

# Dynamics Lunch: Tom Gilat "A proof of the Erdos-Kac theorem by A. Granville and K. Soundararjan"

12:00pm to 1:00pm

## Location:

Manchester faculty club
2019 Jan 09

# Analysis Seminar: Yotam Smilansky (HUJI)

12:00pm to 1:00pm

Title: The distribution of path lengths on directed weighted graphs.
2018 Dec 26

# Analysis Seminar: Rachel Greenfeld (BIU)

12:00pm to 1:00pm

## Location:

Room 70, Ross Building
Title: Fuglede's spectral set conjecture for convex polytopes.
Abstract:
A set \Omega \subset \mathbb{R}^d is called spectral if the space L^2(\Omega) admits an orthogonal basis of exponential functions. Back in 1974, B. Fuglede conjectured that spectral sets could be characterized geometrically as sets which can tile the space by translations. This conjecture inspired extensive research over the years, but nevertheless, the precise connection between the notions of spectrality and tiling, is still a mystery.
2018 Nov 07

# Analysis Seminar: Elik Olami (HUJI) "Homogenization of edge dislocations via de-Rham currents"

12:00pm to 1:00pm

## Location:

Room 70, Ross Building
Title: Homogenization of edge dislocations via de-Rham currents
2018 Nov 06

# Dynamics Lunch: Weikun He "Counterexamples to a conjecture of Woods, after Regev, Shapira and Weiss."

12:00pm to 1:00pm

## Location:

Manchester faculty club
2018 Nov 28

# Analysis Seminar: Netanel Levi "A decomposition of the Laplacian on symmetric metric graphs"

12:00pm to 1:00pm

## Location:

Room 70, Ross Building
Title: A decomposition of the Laplacian on symmetric metric graphs
Abstract
The spectrum of the Laplacian on graphs which have certain symmetry properties can be studied via a decomposition of the operator as a direct sum of one-dimensional operators which are simpler to analyze. In the case of metric graphs, such a decomposition was described by M. Solomyak and K. Naimark when the graphs are radial trees. In the discrete case, there is a result by J. Breuer and M. Keller treating more general graphs.
2018 Dec 12

# Analysis Seminar: Barry Simon "Poncelet’s Theorem, Paraorthogonal Polynomials and the Numerical Range of Truncated GGT matrices"

12:00pm to 1:00pm

## Location:

Room 70, Ross Building
Abstract: During the last 20 years there has been a considerable literature on a collection of related mathematical topics: higher degree versions of Poncelet’s Theorem, certain measures associated to some finite Blaschke products and the numerical range of finite dimensional completely non-unitary contractions with defect index 1. I will explain that without realizing it, the authors of these works were discussing OPUC.