2018 Jun 18

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

(All day)


Eilat Hall, Feldman Building, Givat Ram

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):

* Additive Sparsification and VC dimension
* Multiplicative Sparsification
* Examples: cut weights, cut-dimension of L_1 metrics, general metrics,
                    and their high-dimensional analogues

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 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 Jun 14

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

4:00pm to 5:15pm


Ross 70
Ergodic theoretic methods in the context of homogeneous dynamics have been highly successful in number theoretic and other applications. A lacuna of these methods is that usually they do not give rates or effective estimates. Einseidler, Venkatesh and Margulis proved a rather remarkable quantitative equidistribution result for periodic orbits of semisimple groups in homogenous spaces that can be viewed as an effective version of a result of Mozes and Shah based on Ratner's measure classification theorem.
2018 Dec 12

CS Theory -- Erdős Lecture II: Counting contigency tables


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


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


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


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


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: Michael Chapman, "Conlon's construction of hypergraph expanders"

2:00pm to 3:50pm


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: Shai Evra, "Gromov-Guth embedding complexity"

2:00pm to 3:50pm


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 Jun 04

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

10:00am to 10:50am


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