Pointwise Ergodic Theorems for Bilinear Polynomial Averages

Explore pointwise ergodic theorems for bilinear polynomial averages in this 50-minute lecture. Delve into the proof of pointwise almost everywhere convergence for non-conventional bilinear polynomial ergodic averages, based on joint work with Ben Krause and Terry Tao. Examine normal and pointwise convergence, Furstenberg's correspondence principle, and Burgeon's pointwise convergence. Analyze the summary theorem, limiting behavior, and variational seminorm. Investigate the current state of the art, including important results and questions about pointwise convergence in linear settings. Learn about contributions to Bergelson's conjecture, linear theory, voice inequality, and inverse theorems. Study bilinear averaging operators and ongoing work on commuting transformations.

Intro
Question
Normal and pointwise convergence
How to establish pointwise convergence
Furstenbergs correspondence principle
Burgeons pointwise convergence
Summary theorem
Furstenberg
Behavior limiting behavior
Our variational seminorm
lambda jumps
current state of the art
important result
question about pointwise convergence
pointwise convergence in the linear setting
contribution to thebergers conjecture
proof
linear theory
voice inequality
Inverse theorem
Bilinear averaging operators
Ongoing work
Commuting transformations