Events & Seminars

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
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].
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.

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