Pointwise Convergence of Multiple Ergodic Averages

Abstract: Beginning with the basics of pointwise ergodic theory, I will discuss my forthcoming proof of the Furstenberg conjecture, on the pointwise convergence of the bilinear ergodic averages, $\frac{1}{N} \sum_{n \leq N} T^n f T^{n^2} g,$ where $f,g \in L^{\infty}(X)$ are bounded functions on a probability space $(X,\mu)$, and $T:X \to X$ is a measure-preserving transformation. Joint work with Mariusz Mirek (Rutgers) and Terence Tao (UCLA).

Mathematics

Audience: researchers in the topic

London analysis seminar