Forschungsseminar: Komplexe Geometrie

10.06.2014 Si Li (Boston University)

B-model geometry via Kodaira-Spencer gauge theory

Abstract: Kodaira-Spencer gauge theory (BCOV theory) is proposed in physics as the B-twisted topological closed string field theory. The main purpose of this lecture is to describe certain mathematical aspects of BCOV theory on Calabi-Yau manifolds, which can be viewed as the mirror of Gromov-Witten theory at higher genus. This is developed via Costello's effective renormalization method that will also be briefly introduced in the lecture. As applications, we will discuss higher genus mirror symmetry and also quantum singularity theory.