2018 Jun 07

# Basic Notions: Mike Hochman - "Furstenberg's conjecture on transversality of semigroups and slices of fractal sets" Part II

4:00pm to 5:30pm

## Location:

Ross 70
Second part of the talk from the previous week.
2018 May 31

# Basic Notions: Mike Hochman - "Furstenberg's conjecture on transversality of semigroups and slices of fractal sets" Part I

4:00pm to 5:30pm

## Location:

Ross 70
In 1970, Furstenberg made a number of conjectures about the expansions of real numbers in non-comensurable bases, e.g. bases 2 and 3. The most difficult remains wide open, but several related problems, which can be stated in terms of the dimension theory of certain fractal sets, were recently settled. In the first talk I will try to describe the conjectures and some of what was known. In the second talk I will present Meng Wu's proof of the "slice conjecture" (it was also proved independently by Pablo Shmerkin, and I will try to also say a little about that proof too).
2018 May 21

# HD-Combinatorics Special Day on "Stability in permutations" (organized by Oren Becker)

(All day)

## Location:

Room 130, IIAS, Feldman Building, Givat Ram

Both talks will be given by Oren Becker.
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

# Basic Notions - Benjamin Weiss: "All ergodic systems have the Weak Pinsker property" Part 2

4:00pm to 5:30pm

## Location:

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. I will begin by describing why Jean-Paul formulated this prob-
2018 May 22

# T&G: Elisheva Adina Gamse (Toronto), The moduli space of parabolic vector bundles over a Riemann surface

12:00pm to 1:30pm

## Location:

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

# T&G: Tristan Collins (Harvard), Geometric flows and algebraic geometry

12:00pm to 1:30pm

## Location:

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

# Groups & Dynamics: Anish Gosh (TIFR) - The metric theory of dense lattice orbits

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

# NT&AG: Peng Xu (HUJI), "Supersingular representations of unramifed $U(2,1)$"

2:00pm to 3:00pm

## Location:

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

# T&G: Yael Karshon (Toronto), Old fashioned geometric quantization

12:00pm to 1:30pm

## Location:

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 structures to incorporate the half-form correction into the earlier
2018 May 14

# HD-Combinatorics: Adi Shraibman, "The communication complexity of high-dimensional permutations"

10:00am to 10:50am

## Location:

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: estimating the density Hales-Jewett number, high-dimensional
2018 May 14

# HD-Cominbatorics: Alex Lubotzky, "Stability, approximation and 2nd cohomology"

2:00pm to 4:00pm

## Location:

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

# HD Combinatorics: Jonathan Mosheiff (HUJI), "On the weight distribution of random linear codes"

9:00am to 9:50am

## Location:

Feldman Building, Givat Ram
A random linear (binary) code is a dimension lamba*n (0
2018 Jun 13

# Analysis Seminar: Raz Kupferman (HUJI) "The bending energy of bucked edge-dislocations"

12:00pm to 1:00pm

## Location:

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

# Analysis Seminar: Evgeny Strahov ( HUJI) "Product matrix processes"

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
2018 Jun 07

# Groups & Dynamics seminar Arie Levit (Yale): Critical exponents of invariant random subgroups in negative curvature

10:30am to 12:00pm

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