Events & Seminars

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 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 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 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.
2016 Jan 05

Dynamics lunch: Sebastian Donoso (HUJI) - Automorphism groups of low complexity subshifts

12:00pm to 1:00pm

Location: 

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)
Abstract: The automorphism group of a subshift $(X,\sigma)$ is the group of homeomorphisms of $X$ that commute with $\sigma$. It is known that such groups can be extremely large for positive entropy subshifts (like full shifts or mixing SFT). In this talk I will present some recent progress in the understanding of the opposite case, the low complexity one. I will show that automorphism groups are highly constrained for low complexity subshifts. For instance, for a minimal subshifts with sublinear complexity the automorphism group is generated by the shift and a finite set.

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