腾讯会议：721-201-189
Abstract: In this talk, we will provide a topological condition on a closed manifold, relying on some non-trivial information about its fundamental group, so that any Finsler metric on it admits infinitely many geometrically distinct closed geodesics. This condition potentially covers new examples. Our approach is based on a quantitative perspective of the symplectic cohomology theory, where counting closed geodesics are replaced by counting closed Reeb orbits. Here, the quantitative perspective means that torsions from symplectic cohomology theory play essential roles. We will elaborate on the importance of these torsions from a powerful result called symplectic Smith inequality. This inequality controls the growth of the total number of the closed Reeb orbits in a fixed free homotopy class, especially when this free homotopy class iterates. We emphasize that, different from the classical approaches, our method does not use any index theory. This talk is based on joint work with Egor Shelukhin.
