Dynamical & Probability

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.
2017 Dec 26

Dynamics Seminar: Yuval Peres (Microsoft), "Gravitational allocation to uniform points on the sphere"

2:15pm to 3:15pm

Location: 

Ross 70
Given n uniform points on the surface of a two-dimensional sphere, how can we partition the sphere fairly among them ?    "Fairly" means that each region has the same area.   It turns out that if the given points apply a two-dimensional gravity force to the rest of the sphere, then the basins of attraction for the resulting gradient flow yield such a partition—with exactly equal areas, no matter how the points are distributed. (See the
2017 Nov 28

Dynamics Seminar: Nattalie Tamam (TAU), "Divergent trajectories in arithmetic homogeneous spaces of rational rank two"

2:15pm to 3:15pm

Location: 

Ross 70
In the theory of Diophantine approximations, singular points are ones for which Dirichlet’s theorem can be infinitely improved. It is easy to see that all rational points are singular. In the special case of dimension one, the only singular points are the rational ones. In higher dimensions, points lying on a rational hyperplane are also obviously singular. However, in this case there are additional singular points. In the dynamical setting the singular points are related to divergent trajectories.
2017 Oct 31

Dynamics Seminar: Weikun He (HUJI): Orthogonal projections of discretized sets

2:00pm to 3:00pm

Location: 

Ross 70
In this talk I will discuss a finitary version of projection theorems in fractal geometry. Roughly speaking, a projection theorem says that, given a subset in the Euclidean space, its orthogonal projection onto a subspace is large except for a small set of exceptional directions. There are several ways to quantify "large" and "small" in this statement. We will place ourself in a discretized setting where the size of a set is measured by its delta-covering number : the minimal number of balls of radius delta needed to cover the set, where delta > 0 is the scale.
2017 Dec 12

Dynamics Seminar: Jakub Konieczny, " Automatic sequences, nilsystems and higer order Fourier analysis."

2:15pm to 3:15pm

Location: 

Ross 70
Automatic sequences are one of the most basic models of computation, with remarkable links to dynamics, algebra and logic (among other fields). In the talk, we will explore a point of view inspired by higher order Fourier analysis. Specifically, we will investigate the behaviour of Gowers norms of some automatic sequences, and (almost) classify all automatic sequences given by generalised polynomial fomulas. The tools used will include some non-trivial results concerning dynamics of nilsystems and their connection
2017 Dec 05

Dynamics Seminar: Micheal Hochman (HUJI): Dimension of self-affine sets and measures

2:15pm to 3:15pm

Location: 

Ross 70
I will discuss joint work with Balazs Barany and Ariel Rapaport on the dimension of self-affine sets and measures. We confirm that under mild irreducibility conditions on the generating maps, the dimension is "as expected", i.e. equal to the affinity or Lyapunov dimension. This completes a program started by Falconer in the 1980s. In the first part of the talk I will explain how the Lyapunov dimension arises from Ledrappier-Young formula for self-affine sets, and then explain how additive combinatorics methods can be used to prove that this is the correct dimension.
2017 Nov 21

Dynamics Seminar: Yakov Pesin (PSU), “A geometric approach for constructing equilibrium measures in hyperbolic dynamics”

2:15pm to 3:15pm

Location: 

Ross 70
In the classical settings of Anosov diffeomorphisms or more general locally maximal hyperbolic sets I describe a new approach for constructing equilibrium measures corresponding to some continuous potentials and for studying some of their ergodic properties. This approach is pure geometrical in its nature and uses no symbolic representations of the system. As a result it can be used to effect thermodynamics formalism for systems for which no symbolic representation is available such as partially hyperbolic systems.

Pages