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

When

November 22nd, 2024 | 2:30 p.m. – 3:30 p.m.
Refreshments provided

Where

University Hall 4002

Speaker

Shrey Sanadhya, The Hebrew University of Jerusalem

Abstract

All UAB students, faculty and guests are invited.

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.