Multidimensional local limit theorem in deterministic systems and an application to non-convergence of polynomial multiple averages

Shrey Sanadhya, PhD; Einstein Institute of Mathematics, The Hebrew University of Jerusalem

In this talk, for an ergodic probability preserving system (X,B,m,T), we will discuss the existence of a Z^d valued function , whose corresponding cocycle satisfies the d-dimensional local central limit theorem. As an application, we resolve a question of Huang, Shao and Ye, and Franzikinakis and Host regarding non-convergence in L^2 of polynomial multiple averages of non-commuting zero entropy transformations. We also provide first examples of failure of multiple recurrence for zero entropy transformations along polynomial iterates. This is joint work with Zemer Kosloff.

To participate in this seminar remotely via Zoom, go to https://uiowa.zoom.us/j/99570315915