Gromov-Witten invariants via R-matrix reconstruction

Gromov-Witten theory defines a cohomological field theory (CohFT). Teleman classified semi-simple CohFTs in terms of an ‘R-matrix’. In particular, this allows one to compute higher genus Gromov-Witten invariants of spaces with semi-simple quantum cohomology from their genus 0, 3 point invariants. In this talk I will show that this approach might extend to the non semi-simple setting. The inspiration for this is the Fukaya category and the cyclic open closed map. Time permitting, I will shift focus to open Gromov-Witten invariants, and what information the Fukaya category determines.