The seminar meets on Thursdays, 11:10-12:00, in -101

This Week


Adian Young (BGU)

Random temporo-spatial differentiations

Temporo-spatial 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 non-autonomous dynamical systems. Joint work with Idris Assani.


2023–24–B meetings

Upcoming Meetings

Date
Title
Speaker
Abstract
May 23 Random temporo-spatial differentiations Adian Young (BGU)

Temporo-spatial 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 non-autonomous dynamical systems. Joint work with Idris Assani.

May 30 TBA Lior Tenenbaum (Technion)
Jun 13 TBA Gill Goffer (UCSD)
Jun 27 TBA Ilya Gekhtman (Technion)

Past Meetings

Date
Title
Speaker
Abstract
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.