Dynamical & Probability

2015 Nov 17

Dynamics & probability: Sebastian Donoso (HUJI), "Topological structures and the pointwise convergence of some averages for commuting transformations"

2:00pm to 3:00pm

Location: 

Manchester building, Hebrew University of Jerusalem, (Room 209)
Title: Topological structures and the pointwise convergence of some averages for commuting transformations Abstract: ``Topological structures'' associated to a topological dynamical system are recently developed tools in topological dynamics. They have several applications, including the characterization of topological dynamical systems, computing automorphisms groups and even the pointwise convergence of some averages.  In this talk I will discuss some developments of this subject, emphasizing applications to the pointwise convergence of some averages.
2016 Nov 01

Dynamics & probability

Repeats every week every Tuesday until Tue Jan 24 2017 except Tue Nov 01 2016.
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Location: 

Manchester building, Hebrew University of Jerusalem, (Room 209)
Given a Z^d shift of finite type and a finite range shift-invariant interaction, we present sufficient conditions for efficient approximation of pressure and, in particular, topological entropy. Among these conditions, we introduce a combinatorial analog of the measure-theoretic property of Gibbs measures known as strong spatial mixing and we show that it implies many desirable properties in the context of symbolic dynamics. Next, we apply our
2017 May 16

Dynamics seminar: Karoly Simon (Budepest): Singularity of self-similar measures (Joint with Lajos Vago)

2:00pm to 3:00pm

We consider self-similar  Iterated Function System (IFS) on the line constructed with overlapping cylinders. Recently there have been a number of outstanding results which have suggested that the overlap has dramatic change in the most important properties of the IFS only if there is an exact overlap between some of the cylinders. In this talk, we point out that this is not always the case, at least as far as the absolute continuity of self-similar measures is concerned. Namely, we present some one-parameter families of homogeneous self- similar measures on the line such that
2017 Jan 03

Dynamics & probability: Alon Nishry (U. Michigan): Gaussian complex zeros on the hole event: the emergence of a forbidden region

2:00pm to 3:00pm

Location: 

Manchester building, Hebrew University of Jerusalem, (Room 209)
Consider the Gaussian Entire Function (GEF) whose Taylor coefficients are independent complex-valued Gaussian variables, and the variance of the k-th coefficient is 1/k!. This random Taylor series is distinguished by the invariance of its zero set with respect to the isometries of the complex plane.
2017 Jun 20

Dynamics seminar:Naomi Feldheim (Stanford): Persistence of Gaussian Stationary Processes

2:00pm to 3:00pm

Consider a real Gaussian stationary process, either on Z or on R. That is, a stochastic process, invariant under translations, whose finite marginals are centered multi-variate Gaussians. The persistence of such a process on [0,N] is the probability that it remains positive throughout this interval. The relation between the decay of the persistence as N tends to infinity and the covariance function of the process has been investigated since the 1950s with motivations stemming from probability, engineering and mathematical physics. Nonetheless, until recently, good estimates were
2017 Jan 17

Dynamics & probability: Genadi Levin (HUJI): Monotonicity of entropy for families of interval maps.

2:00pm to 3:00pm

Location: 

Manchester building, Hebrew University of Jerusalem, (Room 209)
I describe a language and set-up for proving monotonicity of entropy for families of interval maps which are defined locally. This can be seen as a local version of Thurston's algorithm. We apply this approach to prove the monotonicity and related results for families that are not covered by other methods (with flat critical point, piecewise linear, Lorenz-type, Arnold family and others) . Joint work with Weixiao Shen and Sebastian van Strien.
2017 Mar 21

Dynamics seminar: Nadav Yesha (Kings College): Pair correlation for quadratic polynomials mod 1

2:00pm to 3:00pm

It is an open question whether the fractional parts of nonlinear polynomials at integers have the same fine-scale statistics as a Poisson point process. We provide explicit Diophantine conditions on the coefficients of degree 2 polynomials under which the limit of an averaged pair correlation density is consistent with the Poisson distribution, using a recent effective Ratner equidistribution result on the space of affine lattices due to Strömbergsson. This is joint work with Jens Marklof.
2016 Nov 29

Dynamics & probability: Ofir David (HUJI), Equidistribution of finite continued fractions.

2:00pm to 3:00pm

Location: 

Manchester building, Hebrew University of Jerusalem, (Room 209)
It is well known that for almost every x in (0,1) its orbit under the Gauss map, namely T(x)=1/x-[1/x], equidistributes with respect to the Gauss-Kuzmin measure. This claim is not true for all x, and in particular it is not true for rational numbers which have finite "orbits" which terminate in 0. In order to still have some equidistribution, we instead group together the orbits corresponding to p/q when q is fixed and (p,q)=1 and ask whether these finite sets equidistribute as q goes to infinity. 
2016 Dec 20

Dynamics & probability: Mike Hochman (HUJI), Dimension of Furstenberg measure of SL_2(R) random matrix products

2:00pm to 3:00pm

Location: 

Manchester building, Hebrew University of Jerusalem, (Room 209)
Given a probability measure mu on the space of 2x2 matrices, there is, under mild conditions, a unique measure nu on the space of lines which is stationary for mu. This measure is called the Furstenberg measure of mu, and is important in many contexts, from the study of random matrix products to recent work on self-affine sets and measures. Of particular importance are the smoothness and dimension of the Furstenberg measure. In this talk I will discuss joint work with Boris Solomyak in which we adapt methods from
2017 May 23

Dynamics seminar: Alex Eskin (Chicago) - On stationary measure rigidity and orbit closures for actions of non-abelian groups

2:00pm to 3:00pm

Abstract: I will describe joint work in progress with Aaron Brown, Federico Rodriguez-Hertz and Simion Filip. Our aim is to find some analogue, in the context of smooth dynamics, of Ratner's theorems on unipotent flows. This would be a (partial) generalization of the results of Benoist-Quint and my work with Elon Lindenstrauss in the homogeneous setting, the results of Brown and Rodriguez-Hertz in dimension 2, and the my results with Maryam Mirzakhani in the setting of Teichmuller dynamics.
2017 Jan 10

Dynamics & probability: Tali Pinsky (TIFR, India): Minimal representatives and the Lorenz equations.

2:00pm to 3:00pm

Location: 

Manchester building, Hebrew University of Jerusalem, (Room 209)
A minimal representative for a dynamical system is a system that has the simplest possible dynamics in its topological equivalence class. This is very much related to "dynamical forcing": when existence of certain periodic orbits forces existence of others. This is quite useful in the analysis of chaotic systems. I'll give examples of minimal representatives in dimensions one two and three. In dimension three, I'll show that the minimal representative for the chaotic Lorenz equations (for the correct parameters) is the geodesic flow on the modular surface. This will be an introductory talk.
2016 Nov 01

Dynamics & probability: Asaf Katz (HUJI): Mixing and sparse ergodic theorems

2:00pm to 3:00pm

Location: 

Manchester building, Hebrew University of Jerusalem, (Room 209)
We consider Bourgain's sparse ergodic theorem for systems where quantitative mixing estimates are present. Focusing on the case of the horocyclic flow, we show how to use such estimates in order to bound the dimension of the exceptional set, providing evidence towards conjectures by N. Shah, G. Margulis and P. Sarnak. Moreover we show that there exists a bound which is independent from the spectral gap. The proof uses techniques from homogeneous dynamics, automorphic representations and number theory.

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