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 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
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:
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 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.
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"
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-
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.