Seminars

2017 Mar 16

Analysis and PDEs: Mayukh Mukherjee (Technion) - Some asymptotic estimates on the geometry of Laplace eigenfunctions

1:00pm to 2:00pm

Location: 

Ross 70
Given a closed smooth Riemannian manifold M, the Laplace operator is known to possess a discrete spectrum of eigenvalues going to infinity. We are interested in the properties of the nodal sets and nodal domains of corresponding eigenfunctions in the high energy limit. We focus on some recent results on the size of nodal domains and tubular neighbourhoods of nodal sets of such high energy eigenfunctions (joint work with Bogdan Georgiev).
2017 Jun 15

Analysis and PDEs, "Quantum state transfer on graphs", G. Lippner (neu)

1:00pm to 2:00pm

Location: 

Ross 70
Title: Quantum state transfer on graphs. Abstract: Transmitting quantum information losslessly through a network of particles is an important problem in quantum computing. Mathematically this amounts to studying solutions of the discrete Schrödinger equation d/dt phi = i H phi, where H is typically the adjacency or Laplace matrix of the graph. This in turn leads to questions about subtle number-theoretic behavior of the eigenvalues of H.
2017 Nov 15

Jerusalem Analysis Seminar: "Operators and random walks", Gady Kozma (Weizmann Institute)

12:00pm to 1:00pm

Location: 

Ross 70 (NOTE LOCATION!)
Abstract: We will discuss the question: for a random walk in a random environment, when should one expect a central limit theorem, i.e. that after appropriate scaling, the random walk converges to Brownian motion? The answer will turn out to involve the spectral theory of unbounded operators. All notions will be defined in the talk. Joint work with Balint Toth.
2017 May 18

Mark Rudelson: Delocalization of the eigenvectors of random matrices.

1:00pm to 2:00pm

Location: 

Ross 70
Abstract: Consider a random matrix with i.i.d. normal entries. Since its distribution is invariant under rotations, any normalized eigenvector is uniformly distributed over the unit sphere. For a general distribution of the entries, this is no longer true. Yet, if the size of the matrix is large, the eigenvectors are distributed approximately uniformly. This property, called delocalization, can be quantified in various senses. In these lectures, we will discuss recent results on delocalization for general random matrices.
2017 Dec 20

Jerusalem Analysis Seminar: "Translation invariant probability measures on the space of entire functions." Adi Glucksam

12:00pm to 1:00pm

Location: 

Ross 70
20 years ago Weiss constructed a collection of non-trivial translation invariant probability measures on the space of entire functions using tools from dynamical systems. In this talk, we will present another elementary construction of such a measure, and give upper and lower bounds for the possible growth of entire functions in the support of such measures.
2016 Dec 22

Analysis and PDE's Seminar -- Percy Deift (Courant)

1:00pm to 2:00pm

Location: 

Ross 70
On the Asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential. T.Bothner, P.Deift, A.Its and I.Krasovsky Abstract: We study the partition function Z of a Coulomb gas of particles with an external potential 2v applied to the particles in an interval of length L. When v is infinite, Z describes the gap probability for GUE eigenvalues in the bulk scaling limit, and has been well-studied for many years. Here we study the the behavior of Z in the full (v,L) plane.
2017 May 17

Mark Rudelson: Delocalization of the eigenvectors of random matrices.

2:00pm to 3:00pm

Location: 

רוס 63
Abstract: Consider a random matrix with i.i.d. normal entries. Since its distribution is invariant under rotations, any normalized eigenvector is uniformly distributed over the unit sphere. For a general distribution of the entries, this is no longer true. Yet, if the size of the matrix is large, the eigenvectors are distributed approximately uniformly. This property, called delocalization, can be quantified in various senses. In these lectures, we will discuss recent results on delocalization for general random matrices.
2017 Dec 13

Jerusalem Analysis Seminar: "Exponential concentration of zeroes of Gaussian stationary functions" Naomi Feldheim (Weizmann Institute)

12:00pm to 1:00pm

Location: 

Ross 70
A Gaussian stationary function (GSF) is a random f: R --> R whose distribution is shift-invariant and all its finite marginals have centered multi-normal distribution. It is a simple and popular model for noise, for which the mean number of zeroes was computed already in the 1940's by Kac and Rice. However, it is far more complicated to estimate the probability of a significant deficiency or abundance in the number of zeroes in a long interval (compared to the expectation). We do so for a specific family of GSFs with additional smoothness and absolutely

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