2016
Nov
22

# Eventss

2017
Apr
27

# PDE and Analysis Seminar: Grzegorz Swiderski (Wroclaw)

1:00pm to 2:00pm

## Location:

Ross 70

Title: Asymptotics of Christoffel functions in an unbounded setting

Abstract:

Consider a measure $\mu$ supported on the real line with all moments finite.

Let $(p_n : n \geq 0)$ be the corresponding sequence of orthonormal

polynomials. This sequence satisfies the three-term recurrence relation

\[

a_{n-1} p_{n-1}(x) + b_n p_n(x) a_n p_{n+1}(x) = x p_n(x) \quad (n > 0)

\]

for some sequences $a$ and $b$.

One defines the $n$th Christoffel function by

\[

\lambda_n(x) = \left[ \sum_{k=0}^n p_k(x)^2 \right]^{-1}.

\]

Abstract:

Consider a measure $\mu$ supported on the real line with all moments finite.

Let $(p_n : n \geq 0)$ be the corresponding sequence of orthonormal

polynomials. This sequence satisfies the three-term recurrence relation

\[

a_{n-1} p_{n-1}(x) + b_n p_n(x) a_n p_{n+1}(x) = x p_n(x) \quad (n > 0)

\]

for some sequences $a$ and $b$.

One defines the $n$th Christoffel function by

\[

\lambda_n(x) = \left[ \sum_{k=0}^n p_k(x)^2 \right]^{-1}.

\]

2017
Dec
06

# Jerusalem Analysis and PDEs seminar: "Asymptotics of the ground state energy for relativistic heavy atoms and molecules" Victor Ivrii (Toronto)

12:00pm to 1:00pm

## Location:

Ross 70.

We discuss sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, without magnetic field or with the self-generated magnetic field, and, in particular, relativistic Scott correction term and also Dirac, Schwinger and relativistic correction terms. In particular, we conclude that the Thomas-Fermi density approximates the actual density of the ground state, which opens the way to estimate the excessive negative and positive charges and the ionization energy.

2016
Nov
10

# Analysis and PDEs - Maurice Duits (KTH) Title: Global fluctuations for non-colliding processes

1:00pm to 2:00pm

## Location:

Ross 70

In this talk we will discuss the global fluctuations for a class of determinantal point processes coming from large systems of non-colliding processes and non-intersecting paths. By viewing the paths as level lines these systems give rise to random (stepped) surfaces. When the number of paths is large a limit shape appears. The fluctuations for the random surfaces are believed to be universally described by the Gaussian Free Field.

2017
Nov
22

# Jerusalem Analysis Seminar: "Inverse Problems with applications to Cryo-Electron Microscopy (cryo-EM)",Roy Lederman

12:00pm to 1:00pm

## Location:

Ross 70

Abstract: Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution".

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).

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.

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.

2016
Jul
30

# לכתוב מייל למורי תכנית הנשיא על פגישה ב-14.8

10:00am to 11:00am

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
Mar
09

# Analysis and PDEs: Iosif Polterovich (Montreal) - Nodal Geometry of Steklov Eigenfunctions

12:00pm to 1:00pm

## Location:

Ross 70

I will present an overview of some recent progress on the study of the nodal sets of Steklov eigenfunctions. In particular, I will discuss sharp estimates on the nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces with boundary obtained in my joint

work with D. Sher and J. Toth.

work with D. Sher and J. 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.

2016
Mar
31

# PDE & Analysis: Mark Ruselson (UMichigan) - No-gaps delocalization for general random matrices.

1:00pm to 2:30pm

## Location:

Ross 70

Title: No-gaps delocalization for general random matrices.

Abstract:

Abstract:

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.

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.