Events & Seminars

2017 May 16

Special dynamics seminar: Ian Morris (Surrey): Equilibrium states of affine iterated function systems

(All day)

Location: 

Equilibrium states of affine iterated function systems
Motivated by the long-standing problem of finding sharp lower estimates for the Hausdorff dimension of self-affine sets, I will describe some recent results on the equilibrium states of the singular value function. These equilibrium states arise as candidates for the measures of maximal Hausdorff dimension on self-affine sets. In particular I will discuss a sufficient condition for uniqueness of the equilibrium state (from joint work with Antti Käenmäki) and an unconditional bound for the number of ergodic equilibrium states (from joint work with Jairo Bochi).
2017 Dec 19

Dynamics Seminar: Asaf Katz (Chicago): "Quantitative disjointness of nilflows and horospherical flows."

2:15pm to 3:15pm

Location: 

Ross 70
In his influential disjointness paper, H. Furstenberg proved that weakly-mixing systems are disjoint from irrational rotations (and in general, Kronecker systems), a result that inspired much of the modern
research in dynamics. Recently, A. Venkatesh managed to prove a quantitative version of this
disjointness theorem for the case of the horocyclic flow on a compact Riemann surface.
2015 Dec 10

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

10:00am to 11:00am

Location: 

Ross building, Hebrew University of Jerusalem, (Room 70)
Abstract
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
2018 Jan 04

Group actions seminar: Ilya Khayutin (IAS/Princeton) - Joint Equidistribution of CM Points

10:30am to 11:30am

Location: 

Ross 70
A sequence of Picard/Galois orbits of special points in a product of arbitrary many modular curves is conjectured to equidistribute in the product space as long as it escapes any closed orbit of an intermediate subgroup. This conjecture encompasses several well-known results and conjectures, including Duke's Theorem, the Michel-Venkatesh mixing conjecture and the equidistribution strengthening of André-Oort in this setting.
2015 Dec 03

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

10:00am to 11:20am

Location: 

Ross building, Hebrew University of Jerusalem, (Room 70)
Abstract:
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

Location: 

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
2017 Dec 21

Groups & Dynamics: Jeremy Kahn (Brown University) - Surface Subgroups in Nonuniform Lattices

10:30am to 11:30am

Location: 

Ross 70
Abstract:
In 2009 the speaker and Vladimir Markovic constructed nearly geodesic surfaces in a given closed hyperbolic 3-manifold M. The construction proceeded by taking all "good pants" in M and matching them at their boundaries to produce a closed surface. I will describe this construction, as well as a new construction with Alexander Wright, of a nearly geodesic surface in the case where M has a cusp. If time permits, I will discuss the potential applications of this construction to higher rank nonuniform lattices and mapping class groups.
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.

Pages