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Explore recent advancements in deriving (open) Gromov-Witten invariants from the Fukaya category in this comprehensive lecture by Kai Hugtenburg from the University of Edinburgh. Delve into the crucial role of the cyclic open-closed map in connecting the cyclic homology of the Fukaya category to S1-equivariant quantum cohomology. Examine R-matrices and their significance in the Givental-Teleman classification of semisimple cohomological field theories, which enable the determination of higher genus Gromov-Witten invariants from genus 0 invariants. Consider the potential extension of this approach beyond the semisimple case and, time permitting, investigate how these results can be applied to obtain open Gromov-Witten invariants from the Fukaya category.
