2015 Dec 24

# Colloquium: Yakov Eliashberg (Stanford) ״Crossroads of symplectic rigidity and flexibility״

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Abstract: The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development. In the talk I will discuss the history of this struggle and describe recent breakthroughs on the flexible side.
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 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.
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 Apr 05

# Dynamics lunch: Shahar Mozes (HUJI) - Margulis inequalities

12:00pm to 1:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)
2016 Mar 08

# Dynamics lunch seminar: Brandon Seward (HUJI): Entropy theory for non-amenable groups (part I)

12:00pm to 1:45pm

## Location:

Ross 70
Entropy was first defined for actions of the integers by Kolmogorov in 1958 and then extended to actions of countable amenable groups by Kieffer in 1975. Recently, there has been a surge of research in entropy theory following groundbreaking work of Lewis Bowen in 2008 which defined entropy for actions of sofic groups. In this mini-course I will cover these recent developments. I will carefully define the notions of sofic entropy (for actions of sofic groups) and Rokhlin entropy (for actions of general countable groups), discuss many of the main results, and go through some of the proofs.