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"
2018 Jun 14

# Groups & Dynamics seminar. Mark Sapir (Vanderbilt): S-machines and their applications

10:30am to 12:00pm

## Location:

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
2018 May 23

# Analysis Seminar: Ori Gurel-Gurevich (HUJI) "Random walks on planar graphs"

12:00pm to 1:00pm

## Location:

Ross Building, Room 70
Title: Random walks on planar graphs Abstract: We will discuss several results relating the behavior of a random walk on a planar graph and the geometric properties of a nice embedding of the graph in the plane (e.g. a circle packing of the graph). An example of such a result is that for a bounded degree graph, the simple random walk is recurrent if and only if the boundary of the nice embedding is a polar set (that is, Brownian motion misses it almost surely). No prior knowledge about random walks, circle packings or Brownian motion is required.
2018 May 08

# T&G: Amitai Yuval (Hebrew University), The Hodge decomposition theorem for manifolds with boundary

12:00pm to 1:30pm

## Location:

Room 110, Manchester Buildling, Jerusalem, Israel
The Hodge decomposition theorem is the climax of a beautiful theory involving geometry, analysis and topology, which has far-reaching implications in various fields. I will present the Hodge decomposition in compact Riemannian manifolds, with or without boundary. The non-empty-boundary case is more interesting, as it requires the formulation of an appropriate boundary condition. As it turns out, the Hodge-Laplacian has two different elliptic boundary conditions generalizing the classical Dirichlet and Neumann conditions, respectively.
2018 May 10

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

4:00pm to 5:30pm

## Location:

Ross 70
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- lem and its significance. Then I will give an aerial view of Tim's
2018 Jun 04

# NT&AG: Hillel Firstenberg (HUJI), "Hyper-modular functions, irrationality of \zeta(3), and algebraic functions over finite fields"

2:00pm to 3:00pm

## Location:

Room 70A, Ross Building, Jerusalem, Israel
Using formal power series one can define, over any field, a class of functions including algebraic and classical modular functions over C. Under simple conditions the power series will have coefficients in a subring of the field - say Z - and this plays a role in Apery's proof of the irrationality of \zeta(3). Remarkably over a finite field all such functions/power series are algebraic. I will call attention to a natural - but open - problem in this area.
2018 May 07

# HD-Combinatorics: Special day on group stability

(All day)

## Location:

Eilat Hall, Feldman Building, Givat Ram

This special day is part of several Mondays that will be dedicated to stability in group theory

09:00 - 11:00 Alex Lubotzky, "Group stability and approximation"

14:00 - 16:00 Lev Glebsky, "Stability and second cohomology"
2018 Jun 26

# Dynamics Lunch: Jasmin Matz (Huji) ״Distribution of periodic orbits of the horocycle flow״

12:00pm to 1:00pm

## Location:

Manchester lounge
An old result of Hedlund tells us that there are no closed orbits for the horocycle flow on a compact Riemann surface M. The situation is different if M is non-compact in which case there is a one-parameter family of periodic orbits for every cusp of M. I want to talk about a result by Sarnak concerning the distribution of the such orbits in each of these families when their length goes to infinity. It turns out that these orbits become equidistributed in M and the rate of convergence can in fact be quantified in terms of spectral properties of the Eisenstein series on M.
2018 May 03

# Special Talk : W Chacholski (Copenhagen) - "What is persistence?"

## Lecturer:

W Chacholski (Copenhagen)
1:15pm to 2:00pm

Ross 63
2018 May 03

# Basic Notions - Alex Lubotzky: "Group stability and approximation"

4:00pm to 5:30pm

## Location:

Ross 70
An old problem (Going back to Turing, Ulam and others) asks about the "stability" of solutions in some algebraic contexts. We will discuss this general problem in the context group theory: Given an "almost homomorphism" between two groups, is it close to a homomorphism?
2018 May 22

# Barak Weiss (TAU): New examples for the horocycle flow on the moduli space of translation surfaces

2:15pm to 3:15pm

A longstanding open question concerning the horocycle flow on moduli space of translation surfaces, is whether one can classify the invariant measures and orbit-closures for this action. Related far-reaching results of Eskin, Mirzakhani and Mohammadi indicated that the answer might be positive. However, in recent work with Jon Chaika and John Smillie, we find unexpected examples of orbit-closures; e.g. orbit closures which are not generic for any measure, and others which have fractional Hausdorff dimension. Such examples exist even in genus 2.
2018 Jun 25

# Combinatorics: Roman Glebov (HU) "Perfect Matchings in Random Subgraphs of Regular Bipartite Graphs"

11:00am to 12:30pm

## Location:

IIAS, room 130, Feldman bldg, Givat Ram
Speaker: Roman Glebov (HU) Title: Perfect Matchings in Random Subgraphs of Regular Bipartite Graphs Abstract: Consider the random process in which the edges of a graph $G$ are added one by one in a random order. A classical result states that if $G$ is the complete graph $K_{2n}$ or the complete bipartite graph $K_{n,n}$, then typically a perfect matching appears at the moment at which the last isolated vertex disappears. We extend this result to arbitrary $k$-regular bipartite graphs $G$ on $2n$ vertices for all $k=\Omega(n)$.
2018 Jun 11

# Combinatorics: Chris Cox (CMU) "Nearly orthogonal vectors"

11:00am to 12:30pm

## Location:

IIAS, Eilat hall, Feldman bldg, Givat Ram
Speaker: Chris Cox, CMU Title -- Nearly orthogonal vectors Abstract -- How can $d+k$ vectors in $\mathbb{R}^d$ be arranged so that they are as close to orthogonal as possible? In particular, define \$\theta(d,k):=\min_X\max_{x
2018 Jun 18

# Combinatorics -- Erdos lecture cancelled; instead (NOTE THE TIME!) :

10:30am to 12:30pm

## Location:

IIAS, Eilat hall, Feldman bldg (top floor), Givat Ram
Speaker: Ilan Newman and Yuri Rabinovich, U.Haifa Title: Sparsifiers - Part I (Part II from 2pm to 4pm, same day and place) Abstract: Time permitting, we plan to discuss the following topics (in this order): 1. * Additive Sparsification and VC dimension * Multiplicative Sparsification * Examples: cut weights, cut-dimension of L_1 metrics, general metrics, and their high-dimensional analogues 2. * Multiplicative Sparsification and Triangular Rank; * Karger-Benczur sparsification of cuts weights 3. * Batson-Spielman-Srivastava sparsification