Quantization formalism in Gromov-Witten theory, Part 1

These will be two expository talks based on work by A. Givental
in the early '00s. I will introduce Gromov-Witten invariants of
a projective variety X and relations among them. Givental noticed
that in genus 0 these relations can be restated in terms of the
symplectic geometry of a Lagrangian cone lying in a symplectic
space H, and that the higher genus invariants are then obtained
by quantization formalism of infinitesimal symplectic operators
on H. I will describe the Lagrangian cone and quantization
formalisms and discuss applications.