2017 Apr 27

# Basic notions: Raz Kupferman

4:00pm to 5:15pm

Abstract: The “geometrization" of mechanics (whether classical, relativistic or quantum) is almost as old as modern differential geometry, and it nowadays textbook material. The formulation of a mathematically-sound theory for the mechanics of continuum media is still a subject of ongoing research. In this lecture I will present a geometric formulation of continuum mechanics, starting with the definition of the fundamental physical observables, e.g., force, deformation, stress and traction. The outcome of this formulation is a generalization of Newton’s "F=ma” equation for continuous media.
2018 Jan 04

# Basic Notions Seminar: Zlil Sela (HUJI) - "Projection complexes, actions on quasi-trees, and applications to mapping class groups of surfaces" (after Bestvina-Bromberg-Fujiwara).

4:00pm to 5:15pm

## Location:

Ross 70
Projection complexes, actions on quasi-trees, and applications to mapping class groups of surfaces (after Bestvina-Bromberg-Fujiwara).
2017 Mar 02

# Basic Notions: Ori Gurel Gurevich (HUJI) - On Smirnov's proof of conformal invariance of critical percolation

4:00pm to 5:00pm

## Location:

Manchester Building, Lecture Hall 2
Abstract:

Let G be an infinite connected graph. For each vertex of G we decide
randomly and independently: with probability p we paint it blue and
with probability 1-p we paint it yellow. Now, consider the subgraph of
blue vertices: does it contain an infinite connected component?

There is a critical probability p_c(G), such that if p>p_c then almost
surely there is a blue infinite connected component and if pp_c or p<p_c.

We will focus on planar graphs, specifically on the triangular
2018 Jan 14

# Kazhdan Sunday seminars: Leonid Polterovich (TAU) "Algebraic methods in symplectic topology"

3:00pm to 5:00pm

## Location:

Ross buildings, Room 70A.
Nick Rozenblyum (Chicago) will talk about Tamarkin's category.
2018 Jan 14

# Kazhdan Sunday seminars: Tomer Schlank (HUJI) "Topics in algebraic topology".

11:00am to 1:00pm

## Location:

Ross buildings, Room 70A.
10:00-11:00 We will have a special lecture on string diagrams by Shaul Barkan 11:00-13:00 Asaf Horev will continue his talk about ambidexterity and duality
2017 Jun 29

# Barry Simon (Caltech)

1:00pm to 2:00pm

Title: Asymptotics for Chebyshev Polynomials of Infinite Gap Sets on the Real Line Abstract: The Chebyshev Polynomials of a compact subset, e, of the complex plane are the monic polynomials minimizing the sup over e. We prove Szego--Widom asymptotics for the Chebyshev Polynomials of a compact subset of R which is regular for potential theory and obeys the Parreau--Widom and DCT conditions. We give indications why these sufficient conditions may also be necessary.
2016 Nov 03

# Analysis and PDEs - Baptiste Devyver (Technion) - "Heat kernel estimates of Schrodinger-type operators"

1:00pm to 2:00pm

## Location:

Ross 70
Let us consider the heat equation: $u_t+Lu=0$ in a domain $\Omega$. Here, $L$ will be a self-adjoint Schrodinger-type operator of the form abla^*
2017 Nov 01

# Jerusalem Analysis Seminar "When do the spectra of self-adjoint operators converge?" Siegfried Beckus (Technion)

12:00pm to 1:00pm

## Location:

Ross 63
Abstract: Given a self-adjoint bounded operator, its spectrum is a compact subset of the real numbers. The space of compact subsets of the real numbers is naturally equipped with the Hausdorff metric. Let $T$ be a topological (metric) space and $(A_t)$ be a family of self-adjoint, bounded operators. In the talk, we study the (Hölder-)continuity of the map assigning to each $t\in T$ the spectrum of the operator $A_t$.
2017 Mar 09

# Analysis and PDEs: Leonid Parnovski (London) - Local Density of states and the spectral function for almost periodic operators

1:00pm to 2:00pm

## Location:

Ross 70
I will discuss the asymptotic behaviour (both on and off the diagonal) of the spectral function of a Schroedinger operator with smooth bounded potential when energy becomes large. I formulate the conjecture that the local density of states (i.e. the spectral function on the diagonal) admits the complete asymptotic expansion and discuss the known results, mostly for almost-periodic potentials.
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 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.
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 in the context of this general framework and present various open problems.
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.