2018
May
30

# Special Wolf Prize lecture: Vladimir Drinfeld (Chicago): Slopes of irreducible local systems

## Lecturer:

Vladimir Drinfeld (Chicago)

11:00am to 12:00pm

## Location:

Kaplan building, Rothberg hall

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2018
May
30

Vladimir Drinfeld (Chicago)

11:00am to 12:00pm

Kaplan building, Rothberg hall

2018
May
21

(All day)

Room 130, IIAS, Feldman Building, Givat Ram

Both talks will be given by

9:00 - 10:50

Title: Proving stability via hyperfiniteness, graph limits and invariant random subgroups

Abstract: We will discuss stability in permutations, mostly in the context of amenable groups. We will characterize stable groups among amenable groups in terms of their invariant random subgroups. Then, we will introduce graph limits and hyperfinite graphings (and some theorems about them), and show how the aforementioned characterization of stability follows.

14:00 - 16:00

2018
May
17

4:00pm to 5:30pm

Ross 70

Second part of the talk from last week:

An ergodic system (X;B; μ; T) is said to have the weak Pinsker

property if for any ε > 0 one can express the system as the direct

product of two systems with the first having entropy less than ε and

the second one being isomorphic to a Bernoulli system. The problem

as to whether or not this property holds for all systems was open for

more than forty years and has been recently settled in the affirmative

in a remarkable work by Tim Austin.

An ergodic system (X;B; μ; T) is said to have the weak Pinsker

property if for any ε > 0 one can express the system as the direct

product of two systems with the first having entropy less than ε and

the second one being isomorphic to a Bernoulli system. The problem

as to whether or not this property holds for all systems was open for

more than forty years and has been recently settled in the affirmative

in a remarkable work by Tim Austin.

2018
May
22

12:00pm to 1:30pm

Room 110, Manchester Buildling, Jerusalem, Israel

Let $\Sigma$ be a Riemann surface of genus $g \geq 2$, and p be a point on $\Sigma$. We define a space $S_g(t)$ consisting of certain irreducible representations of the fundamental group of $\Sigma \setminus p$, modulo conjugation by SU(n). This space has interpretations in algebraic geometry, gauge theory and topological quantum field theory; in particular if Σ has a Kahler structure then $S_g(t)$ is the moduli space of parabolic vector bundles of rank n over Σ.

2018
May
29

12:00pm to 1:30pm

Room 110, Manchester Buildling, Jerusalem, Israel

I will discuss the inverse Monge-Ampere flow and its applications to the existence, and non-existence, of Kahler-Einstein metrics. To motivate this discussion I will first describe the classical theory of the Donaldson heat flow on a Riemann surface, and its relationship with the Harder-Narasimhan filtration of an unstable vector bundle.

2018
May
31

10:30am to 11:30am

Abstract: The classical theory of metric Diophantine approximation is very well developed and has, in recent years, seen significant advances, partly due to connections with homogeneous dynamics. Several problems in this subject can be viewed as particular examples of a very general setup, that of lattice actions on homogeneous varieties of semisimple groups. The latter setup presents significant challenges, including but not limited to, the non-abelian nature of the objects under study.

2018
Jun
11

2:00pm to 3:00pm

Room 70A, Ross Building, Jerusalem, Israel

The recent work of Abe--Henniart--Herzig--Vigneras gives a classification of irreducible admissible mod-$p$ representations of a $p$-adic reductive group in terms of supersingular representations. However, supersingular representations remain mysterious largely, and in general we know them very little. Up to date, there are only a classification of them for the group $GL_2 (Q_p)$ and a few other closely related cases.

2018
May
15

12:00pm to 1:30pm

Room 110, Manchester Buildling, Jerusalem, Israel

I will review the Kostant-Souriau geometric quantization procedure for

passing from functions on a symplectic manifold (classical observables)

to operators on a Hilbert space (quantum observables).

With the "half-form correction" that is required in this procedure,

one cannot quantize a complex projective space of even complex dimension,

and one cannot equivariantly quantize the two-sphere nor any symplectic

toric manifold.

I will present a geometric quantization procedure that uses metaplectic-c

passing from functions on a symplectic manifold (classical observables)

to operators on a Hilbert space (quantum observables).

With the "half-form correction" that is required in this procedure,

one cannot quantize a complex projective space of even complex dimension,

and one cannot equivariantly quantize the two-sphere nor any symplectic

toric manifold.

I will present a geometric quantization procedure that uses metaplectic-c

2018
May
14

2:00pm to 4:00pm

Feldman Building, Givat Ram

We will give a short review of various topics discussed in the first semester and last Monday and then we'll pick the fruits: namely, we will show how to get groups which are no approximated.

2018
May
14

9:00am to 9:50am

Feldman Building, Givat Ram

A random linear (binary) code is a dimension lamba*n (0
Much of the interesting information about a code C is captured by its weight vector. Namely, this is the vector (w_0,w_1,...,w_n) where w_i counts the elements of C with Hamming weight i. In this work we study the weight vector of a random linear code. Our main result is computing the moments of the random variable w_(gamma*n), where 0 < gamma < 1 is a fixed constant and n goes to infinity.

This is a joint work with Nati Linial.

This is a joint work with Nati Linial.

2018
May
14

10:00am to 10:50am

Feldman Buildng, Givat Ram

A k-dimensional permutation is a (k+1)-dimensional array of zeros

and ones, with exactly a single one in every axis parallel line. We consider the

“number on the forehead" communication complexity of a k-dimensional permutation

and ask how small and how large it can be. We give some initial answers to these questions.

We prove a very weak lower bound that holds for every permutation, and mention a surprising

upper bound. We motivate these questions by describing several closely related problems:

and ones, with exactly a single one in every axis parallel line. We consider the

“number on the forehead" communication complexity of a k-dimensional permutation

and ask how small and how large it can be. We give some initial answers to these questions.

We prove a very weak lower bound that holds for every permutation, and mention a surprising

upper bound. We motivate these questions by describing several closely related problems:

2018
Jun
13

12:00pm to 1:00pm

Ross building, room 70

Abstract:

The study of elastic membranes carrying topological defects has a longstanding history, going back at least to the 1950s. When allowed to buckle in three-dimensional space, membranes with defects can totally relieve their in-plane strain, remaining with a bending energy, whose rigidity modulus is small compared to the stretching modulus.

2018
May
30

12:15pm to 1:15pm

Abstract:

I will discuss a family of random processes in discrete time related to products of random matrices (product matrix processes). Such processes are formed by singular values of random matrix products, and the number of factors in a random matrix product plays a role of a discrete time. I will explain that in certain cases product matrix processes are discrete-time determinantal point processes, whose correlation kernels can be expressed in terms of double contour integrals. This enables to investigate determinantal processes for products of ra ndom matrices in

I will discuss a family of random processes in discrete time related to products of random matrices (product matrix processes). Such processes are formed by singular values of random matrix products, and the number of factors in a random matrix product plays a role of a discrete time. I will explain that in certain cases product matrix processes are discrete-time determinantal point processes, whose correlation kernels can be expressed in terms of double contour integrals. This enables to investigate determinantal processes for products of ra ndom matrices in

2018
Jun
14

10:30am to 12:00pm

Ross 70

Title: S-machines and their applications

Abstract: I will discuss applications of S-machines which were first introduced in 1996. The applications include

* Description of possible Dehn functions of groups

* Various Higman-like embedding theorems

* Finitely presented non-amenable torsion-by-cyclic groups

* Aspherical manifolds containing expanders

* Groups with quadratic Dehn functions and undecidable conjugacy problem

Abstract: I will discuss applications of S-machines which were first introduced in 1996. The applications include

* Description of possible Dehn functions of groups

* Various Higman-like embedding theorems

* Finitely presented non-amenable torsion-by-cyclic groups

* Aspherical manifolds containing expanders

* Groups with quadratic Dehn functions and undecidable conjugacy problem

2018
Jun
07

10:30am to 12:00pm

Title : "Critical exponents of invariant random subgroups in negative curvature"