Explore a 51-minute conference talk by Kai Hugtenburg from the Western Hemisphere Virtual Symplectic Seminar on the cyclic open-closed map, u-connections, and R-matrices. Delve into recent advancements in deriving Gromov-Witten invariants from the Fukaya category, focusing on the cyclic open-closed map's role in connecting cyclic homology to S1-equivariant quantum cohomology. Examine R-matrices and their significance in the Givental-Teleman classification of semisimple cohomological field theories, and consider potential extensions beyond the semisimple case. Gain insights into ongoing research on obtaining open Gromov-Witten invariants from the Fukaya category. Engage with audience questions addressing decompositions, the Fukaya category of a point, and specific aspects of the presented material.