2016
Mar
31

# Colloquium: Ronen Eldan (Weizmann) "Interplays between stochastic calculus and geometric inequalities."

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem

Abstract:

2016
Mar
31

2:30pm to 3:30pm

Manchester Building (Hall 2), Hebrew University Jerusalem

Abstract:

2016
Nov
17

2:30pm to 3:30pm

Manchester Building (Hall 2), Hebrew University Jerusalem

We approach the formalism of quantum mechanics from the logician point of view and treat the canonical commutation relations and the conventional calculus based on it as an algebraic syntax of quantum mechanics. We then aim to establish a geometric semantics of this syntax. This leads us to a geometric model, the space of states with the action of time evolution operators, which is a limit of finite models. The finitary nature of the space allows us to give a precise meaning and calculate various classical quantum mechanical quantities.

2015
Dec
03

2:30pm to 3:30pm

Manchester Building (Hall 2), Hebrew University Jerusalem

Title: Extremes of logarithmically correlated fields
Abstract: The general theory of Gaussian processes gives a recipe for estimating the maximum of a random field,
which is neither easy to compute nor sharp enough for obtaining the law of the maximum. In recent years, much effort was invested in understanding the extrema of logarithmically correlated fields, both Gaussian and non-Gaussian. I will explain the motivation, and discuss some of the recent results and the techniques that have been involved in proving them.

2016
Mar
10

3:30pm to 4:30pm

Manchester Building (Hall 2), Hebrew University Jerusalem

This is part of our ongoing effort to develop what we call "High-dimensional combinatorics". We equate a permutation with its permutation matrix, namely an nxn array of zeros and ones in which every line (row or column) contains exactly one 1. In analogy, a two-dimensional permutation is an nxnxn array of zeros and ones in which every line (row, column or shaft) contains exactly one 1. It is not hard to see that a two-dimensional permutation is synonymous with a Latin square. It should be clear what a d-dimensional permutation is, and those are still very partially understood.

2016
Jun
21

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

Let $A$, $B$ be two rational functions of degree at least two on the Riemann sphere.
The function $B$ is said to be semiconjugate to the function $A$ if there exists a non-constant rational function $X$ such that the equality (*) A\circ X=X\circ B holds.
The semiconjugacy relation plays an important role in the classical theory of complex dynamical systems as well as in the new emerging field of arithmetic dynamics. In the talk we present a description of solutions of (*) in terms of two-dimensional orbifolds of non-negative Euler characteristic on the Riemann sphere.

2016
May
31

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

20 years ago Benjy Weiss constructed a collection of non-trivial translation invariant probability measures on the space of entire functions. In this talk we will present a construction of such a measure, and give upper and lower bounds for the possible growth of entire functions in the support of such a measure. We will also discuss "uniformly recurrent" entire functions, their connection to such constructions, and their possible growth. The talk is based on a joint work with Lev Buhovski, Alexander Loganov, and Mikhail Sodin.

2016
Apr
05

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

We give a brief overview on applications of the Poincare's equation to the study of random walk on the the Sierpi ́nski gasket. In particular, we discuss such questions as anomalous diffusion, relation to branching processes and decimation invariance. Metods of the complex analysis and the iteration theory are used to deal with the aforemen-tioned problems.

2016
Nov
03

10:30am to 11:30am

Ross 70

Arithmetic Kleinian groups generated by elements of finite order Abstract: We show that up to commensurability there are only finitely many cocompact arithmetic Kleinian groups generated by rotations. The proof is based on a generalised Gromov-Guth inequality and bounds for the hyperbolic and tube volumes of the quotient orbifolds. To estimate the hyperbolic volume we take advantage of known results towards Lehmer's problem. The tube volume estimate requires study of triangulations of lens spaces which may be of independent interest.

2016
Jan
05

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

Abstract:
We will present an elementary problem and a conjecture regarding percolation on planar graphs suggested by assuming quasi invariance of percolation crossing probabilities under coarse conformal uniformization.

2016
Jun
14

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

Let S be a finite set (the sample space), and
f_i: S -> R functions, for 1 ≤ i ≤ k. Given a k-tuple (v_1,...,v_k) in R^k
it is natural to ask:
What is the distribution P on S that maximizes the entropy
-Σ P(x) log(P(x))
subject to the constraint that the expectation of f_i be v_i?
In this talk I'll discuss a closed formula for the solution P
in terms of a sum over cumulant trees. This is based on a general calculus
for solving perturbative optimization problems due to Feynman, which may be
of interest in its own right.

2016
May
17

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

Abstract: This talk will introduce the notion of Gaussian and almost Gaussian log-correlated fields. These are a class of random (or almost random) functions many of whose statistics are predicted to coincide in a large system-size limit. Examples of these objects include:
(1) the logarithm of the Riemann zeta function on the critical line (conjecturally)
(2) the log-characteristic polynomial of Haar distributed unitary random matrices (and others),
(3) the deviations of Birkhoff sums of substitution dynamical systems (conjecturally)

2016
May
10

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

2016
Mar
15

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

2016
Jun
07

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

2016
Jan
12

1:45pm to 2:45pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

In the paper "Mean dimension, small entropy factors and an
embedding theorem, Inst. Hautes Études Sci. Publ. Math 89 (1999)
227-262", Lindenstrauss showed that minimal systems of mean dimension
less than $cN$ for $c=1/36$ embed equivariantly into the Hilbert cubical
shift $([0,1]^N)^{\mathbb{Z}}$, and asked what is the optimal value
for $c$. We solve this problem by proving that $c=1/2$. The method of
proof is surprising and uses signal analysis sampling theory. Joint
work with Masaki Tsukamoto.