The seminar meets on Thursdays, 11:10-12:00, in -101

## 2018–19–B meetings

Date
Title
Speaker
Abstract
Feb 28 Bounded distance equivalence of aperiodic Delone sets and bounded remainder sets Dirk Frettlöh (Bielefeld university)

Delone sets are generalizations of point lattices: unformly discrete point sets with no large holes. In 1997 Gromov asked whether any Delone set in the Euclidean plane is bilipschitz equivalent to the integer lattice Z^2. A simpler but stronger condition than bilipschitz equivalence is bounded distance equivalence. So it is natural to ask which Delone sets in R^d are bounded distance equivalent to (some scaled copy of) Z^d. This talk gives a gentle introduction to the problem and presents recent results in this context, mostly for cut-and-project sets on the line. In particular we show a connection between bouded remainder sets and cut-and-project sets that are bounded distance equivalent to some lattice.

Mar 7 Local limit theorem for inhomogeneous Markov chains (joint with Dolgopyat) Omri Sarig (Weizmann Institute)

An inhomogeneous Markov chain $X_n$ is a Markov chain whose state spaces and transition kernels change in time. A “local limit theorem” is an asymptotic formula for probabilities of the form

$Prob[S_N-z_N\in (a,b)]$, $S_N=f_1(X_1,X_2)+....+f_N(X_N,X_{N+1})$

in the limit $N\to\infty$. Here $z_N$ is a “suitable” sequence of numbers. I will describe general sufficient conditions for such results.

If time allows, I will explain why such results are needed for the study of certain problems related to irrational rotations.

This is joint work with Dmitry Dolgopyat.

Mar 14 TBA David Lipshutz (Technion)
Mar 21 Purim Holiday
Mar 28 The lower tail for triangles in sparse random graphs Wojciech Samotij (Tel-Aviv University)

Let $X$ denote the number of triangles in the random graph $G(n,p)$. The problem of determining the asymptotic of the rate of the lower tail of $X$, that is, the function $f_c(n,p) = log Pr(X ≤ c E[X])$ for a given $c ∈ [0,1)$, has attracted considerable attention of both the combinatorics and the probability communities. We shall present a proof of the fact that whenever $p >> n^{-1/2}$, then $f_c(n,p)$ can be expressed as a solution to a natural combinatorial optimisation problem that generalises Mantel’s / Turan’s theorem. This is joint work with Gady Kozma.

Apr 4 TBA Federico Vigolo (Weizmann Istitute)
Apr 11 TBA
Apr 18 Passover Holiday
Apr 25 Passover Holiday
May 2 Holocaust Memorial day (talk may be cancelled)
May 9 Independence Day Holiday
May 16 TBA
May 23 TBA
May 30 TBA
Jun 6 TBA
Jun 13 TBA
Jun 20 TBA