Events & Seminars

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.
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 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.
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
2018 Jan 23

Dynamics Lunch: Naomi Feldheim (Weizmann) "How to compute the expected number of zeroes of a random function"

12:00pm to 1:00pm

Location: 

Manchester building lobby

This talk is devoted to the "Kac-Rice formula", which is an explicit way to compute
the expected number of zeroes of a random series with independent Gaussian coefficients.
We will discuss the original proofs of Kac and Rice (1940's),
an elegant geometrical proof due to Edelman and Kostlan (1995), some interesting examples,
and extensions to complex zeroes and eigenvalues of random matrices.

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