May 9

Higher Kazhdan Property and Unitary Cohomology of Arithmetic Groups

Uri Bader (BGU)


May 16

Equidistribution of Discrepancy Sequences (Joint with Dolgopyat)

Omri Sarig (Weizmann Institute of Science)

Let \alpha be an irrational number and let J be a sub interval of [0,1]. The discrepancy sequence of J is D(N), where
D(N):=the number of visits of n\alpha mod 1 to J for 1<n<N minus N 
J 
. 
Weyl’s Equidistribution Theorem says that D(N)=o(N). But this sequence is not necessarily bounded.
I will characterize the irrationals \alpha of bounded type, for which the discrepancy sequence of the interval [0,1/2] is equidistributed on (1/2)Z . This is joint work with Dima Dolgopyat.

May 23

Random temporospatial differentiations

Adian Young (BGU)

Temporospatial differentiations are ergodic averages on a probabilistic dynamical system $(X, \mu, T)$ taking the form $\left( \frac{1}{\mu(C_k)} \int_{C_k} \frac{1}{k} \sum_{j = 0}^{k  1} T^j f \mathrm{d} \mu \right)_{k = 1}^\infty $ where $C_k \subseteq X$ are measurable sets of positive measure, and $f \in L^\infty(X, \mu)$. These averages combine both the dynamics of the transformation and the structure of the underlying probability space $(X, \mu)$. We will discuss the motivations behind studying these averages, results concerning the limiting behavior of these averages and, time permitting, discuss generalizations to nonautonomous dynamical systems. Joint work with Idris Assani.

May 30

Periodic approximation of substitution subshifts

Lior Tenenbaum (Technion)

In studying higher dimensional Schrödinger operators of quasicrystals, one is lead to find
suitable periodic approximations. This means in particular that the spectrum converges as a set
to the limiting spectrum. It turns out that for this to hold, the convergence of the underlying dynamical systems is exactly what is needed. This is the starting point of the present talk.
We focus on aperiodic subshifts defined through symbolic substitutions. These substitution subshifts provide models of aperiodic ordered systems. We find natural sequence candidate of subshifts to approximate the aforementioned substitution subshift. We characterize when these sequences converge, and if so at what asymptotic rate. Some wellknown examples of substitution subshifts are discussed during the talk. We will also discuss the motivation for this characterization, arising from an attempt to study higher
dimensional quasicrystals. This is based on a Joint work with Ram Band, Siegfried Beckus and Felix Pogorzelski.

Jun 13

TBA

Gill Goffer (UCSD)


Jun 20

TBD

Dani Wise (Mcgill)


Jun 27

Stationary random subgroups of hyperbolic groups and applications

Ilya Gekhtman (Technion)

In recent years, the study of measure preserving and stationary actions of Lie groups and hyperbolic groups have produced many geometric consequences. This talk will continue the tradition.
We will show that stationary actions of hyperbolic groups have large critical exponent, namely exponential growth rate more than half of entropy divided the drift of the random walk.
This can be used to prove an interesting geometric result: if the bottom of the spectrum of the Laplacian on a hyperbolic n manifold M is equal to that of its universal cover (or equivalently the fundamental group has exponential growth rate at most (n1)/2) then M has points with arbitrary large injectivity radius.
This is (in some sense the optimal) rank 1 analogue of a recent result of FraczykGelander which asserts that any infinite volume higher rank locally symmetric space has points with arbitrary large injectivity radius.
This is joint work with Arie Levit.

Jul 4

Kepler Sets of Linear Recurrence Sequences

Rishi Kumar (BGU)


Jul 11

Boundary representations of locally compact hyperbolic groups

Michael Glasner (Weizmann Institute of Science)

Given a non elementary locally compact hyperbolic group G equipped with a left invariant metric d one can define a measure on the Gromov boundary called the Patterson Sullivan measure associated to d. This measure is non singular with respect to the G action and contains geometric information on the metric. I will discuss the koopman representations of these actions and sketch a proof of their irreducibility and classification (up to unitary equivalence), generalizing works of Garncarek in the discrete case. I will also describe connections with a recent work of Caprace, Kalantar and Monod on the type I property for hyperbolic groups.

Jul 18

Spacetime Martin boundary and ratiolimit boundariesOnline

Adam DorOn (Haifa University)

Ratiolimit boundaries were first studied for their applications to Toeplitz Calgebras of random walk, but are also interesting in their own right for measuring new types of behavior at infinity. For the purpose of describing Toeplitz Calgebras of random walks, new boundaries need to be identified in more precise terms. One such boundary is the socalled spacetime Martin boundary, as studied by Lalley for random walks on the free group.
In this talk we will discuss ratiolimit boundaries and some work in progress on spacetime Martin boundaries of random walks on discrete groups. The spacetime Martin boundary is related to the notion of stability studied by Picardello and Woess, which elucidates potential descriptions of the spacetime Martin boundaries for random walks on \mathbb{Z}^d and on hyperbolic groups.
