Speaker: Dr. Sicong Zhang (张思聪博士)

Time: 12:00-13:00, 25 March 2021 (Thursday) (Beijing time)

Venue: B414, Lijiao Building, BNU at Zhuhai

Abstract

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.

About Dr. Zhang

Dr. Sicong Zhang was born in Guangzhou, China. He attended Columbia University from 2010 to 2014, and received B.A. in Mathematics with the highest distinction. From 2014 to 2020 he attended Stanford University for doctoral degree in mathematics under the guidance of Yakov Eliashberg, studying the field of symplectic and contact topology. His doctoral thesis deals with foundational aspects of contact homology. After being a lecturer at Stanford in 2020, Dr Zhang is currently an assistant professor at BNU-HKBU United International College.