摘要
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 onP^(2)This survey is based on a three hours lecture series given as part of the Beijing-Zurich moduli workshop in Beijing,9-12 September 2019.
