2018 Jun 25

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

4:30pm to 5:45pm

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...
2018 Dec 12

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

## Lecturer:

Igor Pak (UCLA)
10:30am to 12:00pm

## Location:

Rothberg (CS building) B-220

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.

2019 May 01

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

12:00pm to 1:00pm

## Location:

Ross 70
Title: On tiling the real line by translates of a function 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.
2018 Jun 12

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

1:00pm to 2:30pm

## Location:

Room 110, Manchester Buildling, Jerusalem, Israel
Open Gromov-Witten (OGW) invariants count pseudoholomorphic maps from a Riemann surface with boundary to a symplectic manifold, with constraints that make sure the moduli space of solutions is zero dimensional. In joint work with J. Solomon (2016-2017), we defined OGW invariants in genus zero under cohomological conditions. In this talk, also based on joint work with J. Solomon, I will describe a family of PDEs satisfied by the generating function of our invariants. We call this family the open WDVV equations.
2018 Jun 11

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

10:00am to 10:50am

## Location:

Feldman Building, Givat Ram
In the past decades There has been considerable interest in the probability that two random elements of (finite or certain infinite) 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.
2018 Jun 11

# HD-Combinatorics: Roy Meshulam, "Homology and Expansion of the spherical building"

9:00am to 9:50am

## Location:

Feldman Building, Givat Ram
Let X be the spherical building associated to the group G=GL(n,F) , where F is a finite field. We will survey some results on the homology of X with constant and twisted coefficients, and on the corresponding expansion properties.
2018 Jun 11

# HD-Combinatorics: Michael Chapman, "Conlon's construction of hypergraph expanders"

2:00pm to 3:50pm

## Location:

Feldman Building, Givat Ram
In this talk we recall Conlon's random construction of sparse 2-dim simplicial complexes arising from Cayley graphs of F_2^t . We check what expansion properties this construction has (and doesn't have): Mixing of random walks, Spectral gap of the 1-skeleton, Spectral gap of the links, Co-systolic expansion and the geometric overlap property.
2018 Jun 04

# HD-Combinatorics: Prahladh Harsha, "Local Testability and Expansion"

10:00am to 10:50am

## Location:

Feldman Building, Givat Ram
Locally testable codes are error-correcting codes that admit super-efficient checking procedures. In the first part of the talk, we will see why expander based codes are NOT locally testable. This is in contrast to typical "good" error correcting properties which follow from expansion. We will then see that despite this disconnect between expansion and testability, all known construction of locally testable codes follow from the high-dimensional expansion property of a related complex leaving open an intriguing connection between local-testability and high-dimension
2018 Jun 04

# HD-Combinatorics: Eli Shamir, "Almost optimal Boolean matrix multiplication[BMM] - By Multi-encoding of rows and columns"

9:00am to 9:50am

## Location:

Feldman Building, Givat Ram
Computing R=P.Q ,the product of two mXm Boolean matrices [BMM] is an ingredient of many combinatorial algorithms. Many efforts were made to speed it beyond the standard m^3 steps, without using the algebraic multiplication. To divide the computation task, encoding of the rows and column indices were used (1.1) j by (j1,j2) k by (k1,k2) e.g. using integer p j2=j mod p ,j1=ceiling of j/p. Clearly, the product of the ranges of the digits= m1.m2 - is approximately m. L.Lee’s article reduced BMM to parsing substrings of a fixed string u with
2018 Jun 04

# HD-Combinatorics: Shai Evra, "Gromov-Guth embedding complexity"

2:00pm to 3:50pm

## Location:

Feldman Building, Givat Ram
In this talk we shall review a paper by Gromov and Guth, in which they introduced several ways to measure the geometric complexity of an embedding of simplicial complexes to Euclidean spaces. One such measurement is strongly related to the notion of high dimensional expanders introduced by Gromov, and in fact, it is based on a paper of Kolmogorov and Barzadin from 1967, in which the notion of an expander graph appeared implicitly. We shall show one application of bounded degree high dimensional expanders, and present many more open questions arising from the above mentioned paper.
2018 May 29

# Logic Seminar - Martin Goldstern - "Higher Random Reals"

1:30pm to 3:00pm

The set of real numbers is often identified with
Cantor Space 2^omega, with which it shares many important
properties: not only the cardinality, but also other
"cardinal characteristics" such as cov(null), the smallest
number of measure zero sets needed to cover the whole space,
and similarly cov(meager), where meager="first category";
or their "dual" versions non(meager) (the smallest
cardinality of a nonmeager set) and non(null).

Many ZFC results and consistency results (such as
2018 Jun 26

# Sieye Ryu (BGU): Predictability and Entropy for Actions of Amenable Groups and Non-amenable Groups

2:15pm to 3:15pm

Suppose that a countable group $G$ acts on a compact metric space $X$ and that $S \subset G$ is a semigroup not containing the identity of $G$. If every continuous function $f$ on $X$ is contained in the closed algebra generated by $\{sf : s \in S\}$, the action is said to be $S$-predictable. In this talk, we consider the following question due to Hochman: When $G$ is amenable, does $S$-predictability imply zero topological entropy? To provide an affirmative answer, we introduce the notion of a random invariant order.
2018 May 28

# HD-Combinatorics: Special Day on "Locally testable codes" (organized by Dorit Aharonov and Noga Ron-Zewi)

(All day)

## Location:

Eilat Hall, Feldman Building, Givat Ram
09:00 - 10:50 Noga Ron-Zewi, "Locally testable codes"

14:00 - 14:50 Dorit Aharonov, "Quantum error correcting codes"
​15:00 - 15:50 Dorit Aharonov, " Quantum Locally Testable codes and High dimensional expansion"

Abstract for Noga Ron-Zewi's talk:
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).