seminar

Symplectic geometry and contact geometry had their roots from classical physics, including mechanics, thermal-dynamics, and optics. Starting from Gromov's groundbreaking work in 1985 on pseudo-holomorphic curves, the technique and philosophy has lead to the birth of "symplectic/contact topology" as an active field of research on its own. Some invariants defined using pseudo-holomorphic curve counts, such as Gromov-Witten invariants, Fukaya category, and symplectic field theory, turns out being relevant to modern theoretical physics, namely string theory and quantum field theory.

In this expository talk I will first introduce some basic objects in symplectic and contact topology, how they occurs naturally in classical physics as generalizations of phase spaces, and then explain what pseudo-homolorphic curves are, why in some sense they can be thought of as "gradient flows between critical points", and how they can be used to define symplectic and contact invariants that might have connections to theoretical physics.