Closed Geodesics on Surfaces without Conjugate Points

Explore the fascinating world of closed geodesics on surfaces without conjugate points in this 55-minute mathematics seminar. Delve into Margulis-type asymptotic estimates for counting free homotopy classes of closed geodesics on specific manifolds. Learn how these results apply to all compact surfaces of genus at least 2 without conjugate points. Follow along as speaker Khadim WAR from IMPA/University of Chicago presents joint work with Vaughn Climenhaga and Gerhard Knieper. Gain insights into counting close geodesics, conjugate points, asymptotic bounds, and uniform hyperbolicity. Understand the proof involving Gamma and engage with the Q&A session to deepen your understanding of this complex mathematical topic.

Introduction
Counting close geodesics
Conjugate points
Asymptotic bounds
Uniform hyperbolicity
Proof
Gamma
Questions