2017 Mar 21

# Dynamics lunch: Amir Algom (HUJI): Hausdorff measures of different dimensions are not Borel isomorphic - following András Máthé

12:00pm to 1:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)
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:
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.
2017 May 09

2:00pm to 3:00pm

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.
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.