2017
May
09

# Dynamics seminar: Meng Wu (HUJI)

2:00pm to 3:00pm

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.

2017
Jun
27

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

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

2:00pm to 3:00pm

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

2018
Mar
20

2018
Jan
25

2017
May
11

4:00pm to 5:15pm

Ross 70

The Schmidt Subspace Theorem, its S-arithmetic extension by Schlickewei, and subsequent (rather significant) refinements are highlights of the theory of Diophantine applications and have many applications, some quite unexpected.

2018
Jan
18

2017
Dec
06

12:00pm to 1:00pm

Ross 70

Title: Asymptotics of the ground state energy for relativistic heavy atoms and molecules

2018
Jan
25