Seminar 03.03.22 Griesmer

Title: Rigidity sequences for measure preserving transformations

Speaker: John Griesmer – Colorado School of Mines

Abstract:Let $(X,\mu,T)$ be a probability measure preserving system.  An increasing sequence $(n_k)$ of natural numbers is a rigidity sequence for $(X,\mu,T)$ if $\lim_{k\to\infty} \mu(A\triangle T^{-n_k}A)=0$ for every measurable $A\subset X$.  A classical result says that a generic measure preserving transformation is weak mixing and has a rigidity sequence, and it is natural to wonder which sequences are rigidity sequences for some weak mixing system.  Bergelson, del Junco, Lemańczyk, and Rosenblatt (2012) popularized many problems inspired by this question, and interesting constructions have since been provided by T. Adams; Fayad and Thouvenot; Fayad and Kanigowski; Griesmer; Badea, Grivaux, and Matheron; and Ackelsberg, among others.   This talk will summarize the relevant foundations and survey some recent results. We also consider two variations: union rigidity, where $\lim_{K\to\infty} \mu\Bigl(A\triangle \bigcup_{k>K}T^{-n_k}A\Bigr)=0$ for some  $A$ with $0<\mu(A)<1$, and summable rigidity, where $\sum_{k=1}^\infty \mu(A\triangle T^{-n_k}A)$ converges for some $A$ with $0<\mu(A)<1$.

Zoom link:

Meeting ID: 938 8598 9739

Password: Mixing

Recorded Talk: