2015 Nov 24

# Dynamics & probability: Yaar Salomon (Stonybrook) "The Danzer problem and a solution to a related problem of Gowers"

2:00pm to 3:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Room 209)
The Danzer problem and a solution to a related problem of Gowers Is there a point set Y in R^d, and C>0, such that every convex set of volume 1 contains at least one point of Y and at most C? This discrete geometry problem was posed by Gowers in 2000, and it is a special case of an open problem posed by Danzer in 1965. I will present two proofs that answers Gowers' question with a NO. The first approach is dynamical; we introduce a dynamical system and classify its minimal subsystems. This classification in particular yields the negative answer to Gowers'
2015 Dec 02

# Dynamics & probability: Ron Rosenthal (ETHZ) "Local limit theorem for certain ballistic random walks in random environments"

2:00pm to 3:00pm

## Location:

Ross 70
Title: Local limit theorem for certain ballistic random walks in random environments Abstract: We study the model of random walks in random environments in dimension four and higher under Sznitman's ballisticity condition (T'). We prove a version of a local Central Limit Theorem for the model and also the existence of an equivalent measure which is invariant with respect to the point of view of the particle. This is a joint work with Noam Berger and Moran Cohen.
2015 Nov 10

# Dynamics & probability: Ariel Rapaport (HUJI) " Self-affine measures with equal Hausdorff and Lyapunov dimensions"

2:00pm to 3:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Room 209)
Title: Self-affine measures with equal Hausdorff and Lyapunov dimensions Abstract: Let μ be the stationary measure on ℝd which corresponds to a self-affine iterated function system Φ and a probability vector p. Denote by A⊂Gl(d,ℝ) the linear parts of Φ. Assuming the members of A contract by more than 12, it follows from a result by Jordan, Pollicott and Simon, that if the translations of Φ are drawn according to the Lebesgue measure, then dimHμ=min{D,d} almost surely. Here D is the Lyapunov dimension, which is an explicit constant defined in terms of A and p.
2016 Nov 01

# Dynamics & probability

Repeats every week every Tuesday until Tue Jan 24 2017 except Tue Nov 01 2016.
2:00pm to 3:00pm

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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
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.
2017 Jun 27

# Dynamics seminar:Ohad Feldheim (Stanford): The power of two-choices in reducing discrepancy

2:00pm to 3:00pm

Consider a process in which points are assigned uniformly and independently at random on the interval [0,1]. It is a classical observation that after N points were assigned, the typical discrepancy of the empirical distribution, i.e., the maximum difference between the proportion of points on any interval and the length of that interval, is of order 1/sqrt{N}. Now consider a similar online process in which at every step an overseer is allowed to choose between two independent, uniformly chosen points on [0,1].   -- By how much can the overseer reduce the discrepancy of the selected points?
2017 Mar 07

# Dynamics seminar: Erez Nesharim: Badly approximable vectors in fractals

2:00pm to 3:00pm

In ergodic dynamical systems almost every point is generic. Many times it is interesting to understand how large is the set of non-generic points. In this talk I will present a criterion for a set to have a nonempty intersection with every “regular fractal". We then apply this criterion to show that the set of badly approximable vectors with weights intersects every regular fractal, and put it in the context of diagonalizable actions on homogeneous spaces.  This talk is based on a joint work with Dzmitry Badziahin, Stephen Harrap and David Simmons.
2016 Nov 22

# Dynamics & probability, Vincent Delacroix (Bordeaux): Computing Lyapunov exponents of the Teichmüller flow

2:00pm to 3:00pm

## Location:

Bet Belgia Library, Hebrew University of Jerusalem
The Teichmüller flow acts as a renormalization operator for interval exchange transformations. For this reason its properties give some insight about the dynamics of rational billiards. For example Lyapunov exponents of the Teichmüller flow are tightly related to equidistribution speed in rational billiards. Since the mid 90's M. Kontsevich and A. Zorich started computations of these exponents. After giving some motivating examples for the computation of these exponents and a brief overview of 30 years of intensive research (including works of
2017 Mar 28

2:00pm to 3:00pm

2016 Dec 06

# Dynamics & probability: Lucia Simonelli - Absolutely Continuous Spectrum for Parabolic Flows/Maps

2:00pm to 3:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Room 209)
This talk will discuss some recent developments in the study of the spectral properties of parabolic flows and maps. More specifically, it will focus on the techniques used to determine the spectrum of the time-changes of the horocycle flow and and the effort to generalize these methods to create conditions under which a general parabolic flow/map would be expected to have absolutely continuous spectrum.
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.
2016 Nov 15

# Dynamics & probability: Barak Weiss (TAU): Random walks on homogeneous spaces and diophantine approximation on fractals.

2:00pm to 3:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Room 209)
Abstract: