Events & Seminars

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.
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 11

Basic Notions: Michael Hopkins (Harvard) - Homotopy theory and algebraic vector bundles

4:00pm to 5:15pm

Location: 

Einstein 2
Abstract: This talk will describe joint work with Aravind Asok
and Jean Fasel using the methods of homotopy theory to construct new
examples of
algebraic vector bundles. I will describe a natural conjecture
which, if
true, implies that over the complex numbers the classification
of algebraic
vector bundles over smooth affine varieties admitting an
algebraic cell
decomposition coincides with the classification of topological
complex vector bundles.
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
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. 

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