# Eventss

# HD-Combinatorics Special Day: "Quantum ergodicity and spectral theory with a discrete flavour" (organized by Elon Lindenstrauss and Shimon Brooks)

## Location:

9:00-10:50:

**Shimon Brooks**(Bar Ilan), "Delocalization of Graph Eigenfunctions"

14:00-15:50:

**Elon Lindenstrauss**(HUJI), "Quantum ergodicity on graphs and beyond"

See also the Basic Notions by Elon Lindenstrauss @ Ross 70 (16:30).

Abstract for morning session:

# NT&AG: Gal Porat (HUJI), "Induction and Restriction of $(\varphi,\Gamma)$-Modules"

## Location:

Joint work with Ehud de Shalit.

# T&G: Yaron Ostrover (Tel Aviv), Quantitative symplectic geometry in the classical phase space.

## Location:

# HD-Combinatorics: Special day on sparsification (by Ilan Newman and Yuri Rabinovich)

## Location:

*Special day on sparsification*

Speakers:

**Ilan Newman**and

**Yuri Rabinovich**.

Part I: 10:30 - 12:30

Part II: 14:00 - 15:50

*Abstract for the day:*

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.

# Logic Seminar - Antongiulio Fornasiero - "Generic solutions of exponential equations"

## Location:

dimension n.

If Schanuel Conjecture holds, under some natural conditions on V, we

show that, if V is defined over the rationals, there exists a in C^n

such that (a, exp(a)) is a generic point of V.

# IIAS outreach lecture: Prof. Gil Kalai "Sailing into High Dimensions"

## Lecturer:

## Location:

We will explain what high dimensions are, and describe some questions and answers in geometry and combinatorics of the high dimensional world.

# No Basic notions seminar - deferred to 25.6

# Basic Notions: Elon Lindenstrauss (HUJI) : Effective Equidistribution of closed orbits, property tau, and other applications

## Location:

# Elon Lindenstrauss (HUJI) - Effective Equidistribution and property tau

This is the second of two lectures on the paper Einseidler,, Margulis, Mohammadi and Venkatesh https://arxiv.org/abs/1503.05884. In this second lecture I will explain how the authors obtain using property tau (uniform spectral gap for arithmetic quotient) quantitaive equidistribution results for periodic orbits of maximal semisimple groups. Surprisingly, one can then use this theorem to establish property tau...

# CS Theory -- Erdős Lecture II: Counting contigency tables

## Lecturer:

## Location:

Contingency tables are matrices with fixed row and column sums. They are in natural correspondence with bipartite multi-graphs with fixed degrees and can also be viewed as integer points in transportation polytopes. Counting and random sampling of contingency tables is a fundamental problem in statistics which remains unresolved in full generality.

In the talk, I will review both asymptotic and MCMC approaches, and then present a new Markov chain construction which provably works for sparse margins. I conclude with some curious experimental results and conjectures. Read more about CS Theory -- Erdős Lecture II: Counting contigency tables

# Erdős Lectures: Igor Pak (UCLA)

# Analysis Seminar: Nir Lev (BIU) "On tiling the real line by translates of a function"

## Location:

Abstract: If f is a function on the real line, then a system

of translates of f is said to be a << tiling >> if it constitutes

a partition of unity. Which functions can tile the line by

translations, and what can be said about the structure of the

tiling? I will give some background on the problem and present

our results obtained in joint work with Mihail Kolountzakis.

# T&G: Sara Tukachinsky (IAS), An enhanced quantum product and its associativity relation

## Location:

# HD-Combinatorics: Aner Shalev, "Probabilistically nilpotent groups"

## Location:

groups commute.

I will describe new works (by myself and by others) on probabilistically nilpotent groups, namely groups in which the probability that [x_1,...,x_k]=1 is positive/bounded away from zero.

It turns out that, under some natural conditions,

these are exactly the groups which have a finite/bounded index

subgroup which is nilpotent of class < k.

The proofs have some combinatorial flavor.