POINTWISE ERGODIC THEOREM ALONG PRIMES

Abstract: In this talk, we will be exploring the pointwise convergence of ergodic averages along the primes. Our discussion will begin by explaining the contributions of Birkhoff, as well as the efforts made by Bourgain and Wierdl in this direction, which was concluded by Mirek’s proof of pointwise ergodic convergence for primes. Additionally, we will be presenting some of our own results on structure theorems in the endpoint case Lplogq, along with a pointwise ergodic theorem in the Gaussian setting. Moving forward, we will briefly mention the breakthrough result made by Krause-Mirek-Tao on bilinear ergodic averages. This will be departing point in our current project on the pointwise ergodic theorem for bilinear averages along prime numbers. If time allows, we will provide a toy model example in linear theory, which will demonstrate a typical method used in this area of study.

algebraic geometrynumber theory

Audience: researchers in the topic

Comments: password is 848084.

FGC-HRI-IPM Number Theory Webinars

Series comments: password is 848084