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.