Seminar 11.10.22 Kuca – Virtually

Title: Multiple ergodic averages along polynomials and joint ergodicity

Speaker:  Borys Kuca – University of Crete

Abstract: Furstenberg’s dynamical proof of the Szemerédi theorem initiated a thorough examination of multiple ergodic averages, laying the grounds for a new subfield within ergodic theory. Special attention has been paid to averages of commuting transformations with polynomial iterates owing to their central role in Bergelson and Leibman’s proof of the polynomial Szemerédi theorem. Their norm convergence has been established in a celebrated paper of Walsh, but for a long time, little more has been known due to obstacles encountered by existing methods. Recently, there has been an outburst of research activity which sheds new light on their limiting behaviour. I will discuss a number of novel results, including new seminorm estimates and limit formulas for these averages. Additionally, I will talk about new criteria for joint ergodicity of general families of integer sequences whose potential utility reaches far beyond polynomial sequences. The talk will be based on two recent papers written jointly with Nikos Frantzikinakis.

Zoom link:

Meeting ID: 919 4381 2487

Password: Mixing

Link of recorded talk: