Ergodicity and Horocycle Ergodic Averages on Compact Spaces - Lecture 2

Explore the second lecture in a six-part series on horocycle flows and their time-changes, focusing on ergodicity and precise asymptotics of horocycle ergodic averages on compact spaces. Delve into the mathematical foundations of homogeneous unipotent flows and their parabolic dynamics, examining how these fundamental concepts contribute to our understanding of ergodic theory. Learn about the behavior of horocycle flows as prime examples of uniformly parabolic dynamics, and discover how smooth time-changes serve as simple yet intriguing perturbations that maintain parabolic characteristics. Part of the Simons Semester on Dynamics, this hour-long lecture builds upon the foundational concepts introduced in the first session and sets the stage for exploring mixing properties, time-changes, rigidity, and applications beyond SL2(R) in subsequent lectures.