2016 Dec 22

# Colloquium: Itai Ben Yaakov (Université Claude Bernard - Lyon 1) "Full globally valued fields"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
The Globally Valued Fields (GVF) project is a joint effort with E. Hrushovski to understand (standard and) non-standard global fields - namely fields in which a certain abstraction of the product formula holds. One possible motivation is to give a model-theoretic framework
for various asymptotic distribution results in global fields.
Formally, a GVF is a field together with a "valuation" in the additive group of an L^1 space, such that the integral of v(a) vanishes for every non-zero a .
2016 Feb 25

# Colloquium: Michah Sageev (Technion) "The geometry of CAT(0) cube complexes"

3:30pm to 4:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Abstract: We will discuss the geometry of CAT(0) (non-positively curved) cube complexes and groups which act on them. In particular, we will focus on "hyperbolic-like" behavior in such spaces.
2016 May 19

# Colloquium: Aner Shalev (Hebrew University) "Probability, growth and complexity in groups"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
I will describe some recent advances in the study of
infinite and finite groups, related to probability,
growth and complexity.
for linear groups, and present extensions and variations,
including a joint work with Larsen on a probabilistic Tits alternative. This is related to the notion of probabilistic
identities, and related results and open problems will be
mentioned.
I will then discuss approximate subgroups, an important
result by Breuillard-Green-Tao and Pyber-Szabo, and
2015 Nov 05

# Colloquium: Gady Kozma (Weizmann), "Riesz bases of exponentials"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Title: Riesz bases of exponentials.
Abstract:
2016 Dec 08

# Colloquium: Gordon Slade (UBC) "Critical phenomena in statistical mechanics"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
The subject of phase transitions and critical phenomena in statistical mechanics is a rich source of interesting and difficult mathematical problems. There has been considerable success in solving such problems for systems in spatial dimension 2, or in high dimensions, but not in dimension 3. This lecture is intended to provide an introduction to recent work that employs a renormalisation group method to study spin systems and self-avoiding walk in dimension 4 (joint with Bauerschmidt and Brydges), as well as long-range versions of these models in dimensions 1,2,3 via an "epsilon expansion."
2015 Dec 31

# Colloquium : Jasmin Matz, "Distribution of Hecke eigenvalues for GL(n)"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Abstract:
A classical problem in the theory of automorphic forms is to count the
number of eigenvalues of the Laplacian acting on cuspidal functions on
the quotient of the upper half plane by a lattice R. For R=SL(2,Z) (or a
congruence subgroup thereof) the answer is given by Selberg's Weyl law
while for the higher rank situation it was established by Mueller and
Lindenstrauss-Venkatesh.
Additional to the Laplacian there is another large family of operators,
namely the Hecke operators attached to SL(2,Z). Sarnak proved that the
2016 Apr 07

# Colloquium: Lai-Sang Young (Courant) "Measuring Dynamical Complexity"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
I will discuss, for differentiable dynamical systems, three ways to capture dynamical complexity:
hyperbolicity, which measures the sensitivity of dependence on initial conditions.
entropy, which measures the predictability of future dynamical events in the sense of information theory.
the speed of correlation decay or equivalently the rate at which memory is lost.
2016 Jan 12

# Dynamics & prob. [NOTE SPECIAL TIME!!], Yonatan Gutman (IMPAN) - Optimal embedding of minimal systems into shifts on Hilbert cubes

1:45pm to 2:45pm

## Location:

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.
2016 Jun 21

# Dynamics & probability: Fedor Pakovitch - On semiconjugate rational functions

2:00pm to 3:00pm

## Location:

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.
2016 May 31

# Dynamics & probability: Adi Glücksam (TAU): Translation invariant probability measures on the space of entire functions

2:00pm to 3:00pm

## Location:

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

# Dynamics & probability: Grisha Derfel (BGU): “Diffusion on fractals and the Poincare's functional equation"

2:00pm to 3:00pm

## Location:

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

# Groups and dynamics - Misha Belolipetsky

10:30am to 11:30am

## Location:

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

# Dynamics & probability: Itai Benjamini (Weizmann) - Coarse uniformization and percolation

2:00pm to 3:00pm

## Location:

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

# Dynamics & probability: Amitai Zernik (HUJI): A Diagrammatic Recipe for Computing Maxent Distributions

2:00pm to 3:00pm

## Location:

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
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

# Dynamics & probability: Elliot Paquette (Weizmann) - Almost gaussian log-correlated fields

2:00pm to 3:00pm

## Location:

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)