EVENT DETAILS AND ABSTRACT

Title: Non-conventional ergodic averages
Speaker: Professor Bryna Kra
Speaker Info: Penn State
Brief Description:
Special Note:
Abstract:

Erdos and Turan conjectured that any set of integers with positive upper density contains arithmetic progressions of arbitrary length. Szemer\'edi proved this using combinatorial methods. A few year later, Furstenberg gave a new proof using "non-conventional" ergodic averages that gave birth to the new field of ergodic Ramsey Theory. I will give an overview of recent results on non-conventional ergodic averages, including averages evaluated along arithmetic progressions, at polynomial values and along combinatorial cubes. For each average, the average behavior turns out to be algebraic in nature. More precisely, the dynamics of a translation on homogeneous spaces of nilpotent Lie groups determine the limiting behavior of these averages.