Scattering diagrams, sheaves, and curves

Abstract

We review the recent proof of the N. Takahashi's conjecture on genus 0 Gromov-Witten invariants of (P 2 , E), where E is a smooth cubic curve in the complex projective plane P 2 . The main idea is the use of the algebraic notion of scattering diagram as a bridge between the world of Gromov-Witten invariants of (P 2 , E) and the world of moduli spaces of coherent sheaves on P 2 . Using this bridge, the N. Takahashi's conjecture can be translated into a manageable question about moduli spaces of coherent sheaves on P 2 . This survey is based on a three hours lecture series given as part of the