Title: The closed geodesic problem
Speaker: Barry Minemyer (OSU)
Seminar URL: https://research.math.osu.edu/ggt/
Abstract: A famous result due to Gromoll and Meyer states that if the sequence of Betti numbers of the free loop space of a compact simply connected Riemannian manifold is unbounded, then there exists infinitely many geometrically distinct closed geodesics on that manifold. This result, in conjunction with results due to Klingenberg, Vigue-Porrier, and Sullivan, has led to the conjecture that every compact Riemannian manifold admits infinitely many distinct closed geodesics.
In this talk I will outline the proof of the Gromoll-Meyer result and discuss some ideas of how to generalize this result to a different setting. This is joint work with Pedro Ontaneda.
