2015
Dec
15

# Dynamics & probability: Omri Solan (TAU) - Divergent trajectories in SL_3(R)/SL_3(Z)

2:00pm to 4:30pm

## Location:

Manchester building, Hebrew University of Jerusalem, 209

Abstract:

2015
Dec
15

2:00pm to 4:30pm

Manchester building, Hebrew University of Jerusalem, 209

Abstract:

2015
Nov
17

2:00pm to 3:00pm

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

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

2:00pm to 3:00pm2:00pm to 3:00pm

2:00pm to 3:00pm

2:00pm to 3:00pm

2:00pm to 3:00pm

2:00pm to 3:00pm

2:00pm to 3:00pm

2:00pm to 3:00pm

2:00pm to 3:00pm

2:00pm to 3:00pm

2:00pm to 3:00pm

2:00pm to 3:00pm

2:00pm to 3:00pm

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

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

2:00pm to 3:00pm

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

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

2:00pm to 3:00pm

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

2:00pm to 3:00pm

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

Abstract:

2017
Mar
21

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

2:00pm to 3:00pm

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

2:00pm to 3:00pm

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

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

2:00pm to 3:00pm

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

2:00pm to 3:00pm

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.