2017 May 25

# 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 Jun 16

# Jerusalem Analysis and PDEs - Gilbert Weinstein (Ariel)

1:00pm to 2:00pm

## Location:

Ross 70
Title: Harmonic maps with prescribed singularities and applications to general relativity
Abstract: We will present a general theory of existence and uniqueness for harmonic maps with prescribed singularities into Riemannian manifolds with non-positive curvature. The singularities are prescribed along submanifolds of co-dimension 2. This result generalizes one from 1996, and is motivated by a number of recent applications in general relativity including:
* a lower bound on the ADM mass in terms of charge and angular momentum for multiple black holes;
2017 Nov 08

# Jerusalem Analysis Seminar: "To infinity and back (a bit)", Jonathan Breuer (HUJI)

12:00pm to 1:00pm

## Location:

Ross 63

Let H be a self-adjoint operator defined on an infinite dimensional Hilbert space. Given some
spectral information about H, such as the continuity of its spectral measure, what can be said about
the asymptotic spectral properties of its finite dimensional approximations? This is a natural (and
general) question, and can be used to frame many specific problems such as the asymptotics of zeros of
orthogonal polynomials, or eigenvalues of random matrices. We shall discuss some old and new results
2016 Dec 29

# Analysis and PDEs Seminar: Svetlana Jitomirskaya (UC Irvine)

1:00pm to 2:00pm

## Location:

Ross 70
Title: Sharp arithmetic spectral transitions and universal hierarchical structure of quasiperiodic eigenfunctions.
Abstract: A very captivating question in solid state physics
is to determine/understand the hierarchical structure of spectral features
of operators describing 2D Bloch electrons in perpendicular magnetic
fields, as related to the continued fraction expansion of the magnetic
flux. In particular, the hierarchical behavior of the eigenfunctions of
the almost Mathieu operators, despite signifi cant numerical studies and
2017 May 24

# 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 27

# Jerusalem Analysis Seminar: "Optimal Gaussian Partitions", Elchanan Mossel (MIT)

12:00pm to 1:00pm

## Location:

Ross 70

How should we partition the Gaussian space into k parts in a way that minimizes Gaussian surface area, maximize correlation or simulate a specific distribution. The problem of Gaussian partitions was studied since the 70s first as a generalization of the isoperimetric problem in the context of the heat equation. It found a renewed interest in the context of the double bubble theorem proven in geometric measure theory and due to connection to problems in theoretical computer science and social choice theory.

2016 Nov 22

# SPECIAL Analysis and PDEs seminar -D. Fajman "Dynamics of Spacetime — Einstein’s equations as a geometric flow."

11:00am to 12:00pm

Ross 70
Abstract:
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
$\lambda_n(x) = \left[ \sum_{k=0}^n p_k(x)^2 \right]^{-1}.$
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).
2017 Nov 16

2:00pm to 3:00pm

2017 Jun 29

# Special Seminar: Ayala Byron (HUJI) "Homogeneity of torsion-free hyperbolic groups"

2:00pm to 3:00pm

## Location:

Ross 70

Abstract:
A (countable) group G is homogeneous if whenever g,h are tupples of the same type in G, there is an automorphism of G sending g to h.
We give a characterization of freely-indecomposable torsion-free hyperbolic groups which are homogeneous, in terms of a particular decomposition as a graph of groups - their JSJ decomposition. This is joint work with Chloe Perin.
2017 Aug 09

# Topology and Geometry Seminar: "Bordered methods in knot Floer homology" Peter Ozsvath, Princeton University

12:00pm to 1:00pm

## Location:

Ross 70A
Abstract: Knot Floer homology is an invariant for knots in the three-sphere defined using methods from symplectic geometry. I will describe a new algebraic formulation of this invariant which leads to a reasonably efficient computation of these invariants. This is joint work with Zoltan Szabo.