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

3:00pm to 5:00pm

Ross buildings, Room 70A.

Nick Rozenblyum (Chicago) will talk about Tamarkin's category.

2017
Oct
22

(All day)

2018
Jan
14

11:00am to 1:00pm

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
Dec
13

12:00pm to 1:00pm

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

2016
Nov
17

1:00pm to 2:00pm

Ross 70

Abstract. We will give a sketch of the proof of the fact formulated in the title.

2017
Mar
23

1:00pm to 2:00pm

Ross 70

Title: a random Schroedinger operator stemming from reinforced process
Abstract:
We will explain the relationship between a toy model to Anderson localization, called the H^{2|2} model (according to Zirnbauer) and edge reinforced random walk.
The latter is a random walk in which, at each step, the walker prefers traversing previously visited edges, with a bias proportional to the number of times the edge was traversed. Recent study on this random walk showed that it is equivalent to Zirnbauer's model and we will show some consequences once this equivalence is established.

2017
Jun
29

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

1:00pm to 2:00pm

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

12:00pm to 1:00pm

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

1:00pm to 2:00pm

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.

2017
May
25

1:00pm to 2:00pm

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

1:00pm to 2:00pm

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

12:00pm to 1:00pm

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

1:00pm to 2:00pm

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

2:00pm to 3:00pm

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.