2016 Nov 03

# Colloquium: T.N.Venkataramana (Tata Institute) "Monodromy Groups and Arithmetic Groups"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
To a linear differential equation on the projective line with finitely many points of singularities, is associated a monodromy group; when the singularities are "reguar singular", then the monodromy group gives more or less complete information about the (asymptotics of the ) solutions. The cases of interest are the hypergeometric differential equations, and there is much recent work in this area, centred around a question of Peter Sarnak on the arithmeticity/thin-ness of these monodromy groups. I give a survey of these recent results.
2015 Nov 19

# Colloquium: Shmuel Weinberger (Chicago), "The Quantitative challenge to topology"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Serre's thesis and its aftermath rolled in a golden age of algebraic topology which led to the impression that we can really understand (necessarily highly nonlinear) maps from one space to another. With the work of Thom on cobordism and Smale on immersions and the Poincare conjecture, a paradigm developed where geometric problems would be solved by reduction to algebraic topological ones.
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 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 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

# 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)
2016 May 10

# Dynamics & probability: Tamar Ziegler (HUJI) - Concatenating characteristic factors

2:00pm to 3:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Room 209)
2016 Mar 15

# Dynamics & probability: Mike Hochman "Dimension of Furstenberg measure for SL_2(R) random matrix products"

2:00pm to 3:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Room 209)
2016 Jun 07

# Dynamics & probability: Hillel Furstenberg (HUJI): Algebraic numbers and homogeneous flows

2:00pm to 3:00pm

## Location:

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