Events & Seminars

2015 Nov 05

Groups & Dynamics : Ilya Khayutin (HUJI)

9:45am to 11:00am

Location: 

Manchester building, Hebrew University of Jerusalem, (Room 209)
Title: Arithmetic of Double Torus Quotients and the Distribution of Periodic Torus Orbits Abstract: In this talk I will describe some new arithmetic invariants for pairs of torus orbits on inner forms of PGLn and SLn. These invariants allow us to significantly strengthen results towards the equidistribution of packets of periodic torus orbits on higher rank S-arithmetic quotients. An important aspect of our method is that it applies to packets of periodic orbits of maximal tori which are only partially split.
2016 Apr 10

Dvoretzky lecture 2: Lai-Sang Young (Courant) "Proving the positivity of Lyapunov exponents"

4:00pm to 5:00pm

Location: 

Lecture hall 2
A signature of chaotic behavior in dynamical systems is sensitive dependence on initial conditions, and Lyapunov exponents measure the rates at which nearby orbits diverge. One might expect that geometric expansion or stretching in a map would lead to positive Lyapunov exponents. This, however, is very difficult to prove - except for maps with invariant cones (or a priori separation of expanding and contracting directions).
2015 Dec 17

Groups & dynamics: Robert Hough (IAS) - Mixing and cut-off on cyclic groups

12:00pm to 1:00pm

Location: 

Einstein 110
Consider a sequence of random walks on $\mathbb{Z}/p\mathbb{Z}$ with symmetric generating sets $A= A(p)$. I will describe known and new results regarding the mixing time and cut-off. For instance, if the sequence $|A(p)|$ is bounded then the cut-off phenomenon does not occur, and more precisely I give a lower bound on the size of the cut-off window in terms of $|A(p)|$. A natural conjecture from random walk on a graph is that the total variation mixing time is bounded by maximum degree times diameter squared.
2015 Nov 19

Groups & dynamics: Lei Yang (HUJI) "Equidistribution of expanding translates of curves in homogeneous spaces and Diophantine approximation"

10:00am to 11:00am

Location: 

Ross 70
Title: Equidistribution of expanding translates of curves in homogeneous spaces and Diophantine approximation. Abstract: We consider an analytic curve $\varphi: I \rightarrow \mathbb{M}(n\times m, \mathbb{R}) \hookrightarrow \mathrm{SL}(n+m, \mathbb{R})$ and embed it into some homogeneous space $G/\Gamma$, and translate it via some diagonal flow
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. I will discuss Venkatesh's disjointness result and present a generalization of this result to more general actions of nilpotent groups, utilizing structural results about nilflows proven by Green-Tao-Ziegler.
2017 Feb 28

Dynamics seminar: Emmanuel Roy (Paris 13): Ergodic splittings of Poisson processes

2:00pm to 3:00pm

If N denotes a Poisson process, a splitting of N is formed by two point processes N_1 and N_2 such that N=N_1+N_2. If N_1 and N_2 are independent Poisson processes then the splitting is said to be Poisson and such a splitting is always available (We allow the possibility to enlarge the ambient probability space). In general, a splitting is not Poisson but the situation changes if we require that the distributions of the point processes involved are left invariant by a common underlying map that acts at the level of each point of the processes.
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 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.
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.

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