Events & Seminars

2015 Dec 03

Groups & dynamics: Shmuel Weinberger (Chicago) - Borel and the symmetry of locally symmetric manifolds. I

10:00am to 11:20am


Ross building, Hebrew University of Jerusalem, (Room 70)
Borel studied the topological group actions that are
possible on locally symmetric manifolds. In these two talks, I will
explain Borel's work and interpret these results as a type of rigidity
statement very much related to the well-known Borel conjecture of high
dimensional topology. In particular, I will give the characterization
of locally symmetric manifolds (of dimension not 4) which have a
unique maximal conjugacy of finite group of orientation preserving
homeomorphisms, due to Cappell, Lubotzky and myself. We will then
2017 May 25

Group actions/dynamics seminar: Sebastián Donoso (University of O'Higgins, Chile) Quantitative multiple recurrence for two and three transformations

10:00am to 11:00am


Ross 70
In this talk I will provide some counter-examples for quantitative multiple
recurrence problems for systems with more than one transformation.  For
instance, I will show that there exists an ergodic system
$(X,\mathcal{X},\mu,T_1,T_2)$ with two commuting transformations such that
for every $\ell < 4$ there exists $A\in \mathcal{X}$ such that 
\[ \mu(A\cap T_1^n A\cap T_2^n A) < \mu(A)^{\ell} \] 
for every $n \in \mathbb{N}$. 
The construction of such a system is based on the study of ``big'' subsets
2018 Jan 09

Dynamics Lunch: Raimundo Briceno (TAU) "A Breiman type theorem for Gibbs measures"

12:00pm to 1:00pm

We will review a Breiman type theorem for Gibbs measures due to Gurevich and Tempelman. For a translation invariant Gibbs measure on a suitable translation invariant configuration set X \subset S^G, where G is an amenable group and S is a finite set, we will prove the convergence of the Shannon-McMillan-Breiman ratio on a specific subset of "generic" configurations. Provided that the above Gibbs measure exists, we also prove the convergence in the definition of pressure and the fact that this Gibbs measure is an equilibrium state.
2018 Jan 02

Dynamics Lunch: Ohad Feldheim (HUJI) "Finitely dependent proper colouring of Z"

12:00pm to 1:00pm

An M-dependent process X(n) on the integers, is a process for which every event concerning with X(-1),X(-2),... is independent from every event concerning with X(M),X(M+1),...
Such processes play an important role both as scaling limits of physical systems and as a tool in approximating other processes.
A question that has risen independently in several contexts is:
"is there an M dependent proper colouring of the integer lattice for some finite M?"
2017 Dec 05

Dynamics Lunch: Jon Aaronson (TA) "Title: "Classical probability theory" for processes generated by expanding C^2 interval maps via quasicompactness."

12:00pm to 1:00pm

Abstract: It was noticed in the 30's by Doeblin & Forte that Markov
operators with "chains with complete connections"
act quasi-compactly on the Lipschitz functions. These are operators
like the transfer operators of certain expanding
C^2 interval maps (e.g. the square of Gauss map).
It is folklore that stochastic processes generated by smooth
observables under these maps satisfy many of the results
of "classical probability theory" (e.g. CLT, Chernoff inequality).
I'll try to explain some of this in a "lunchtime" mode.