Reeb Orbits Frequently Intersecting a Symplectic Surface

Explore a mathematics seminar where Michael Hutchings from UC Berkeley delves into the intricate relationship between Reeb orbits and symplectic surfaces in contact three-manifolds. Learn about the existence of Reeb orbits intersecting with the interior of symplectic surfaces, contingent on specific rotation number inequalities of boundary Reeb orbits. Discover how to calculate explicit lower bounds for intersection frequencies, defined as the ratio of intersection counts to symplectic action. Examine the application of these findings to global surfaces of section, leading to expanded understanding of the connection between mean action and Calabi invariant in area-preserving surface diffeomorphisms.