Introduction to Gromov--Witten invariants and Gopakumar--Vafa invariants 2/2
ABSTRACT
In these talks, we study the basic ideas of Gromov--Witten invariants for a CY 3-fold, which arise from a topological string theory. Starting from mathematical preliminaries, we'll discuss the simplest examples of GW invariants. We will also discuss why it is so difficult to compute any non-trivial GW invariants.
We will also study some cousins of GW invariants, mainly focusing on Gopakumar--Vafa invariants and its mathematical definition in some simple cases. Both GW and GV invariants conjecturally contain equivalent data for a CY 3-fold. Physically, however, they count different, seemingly-unrelated, things from various string theories.