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Explore a comprehensive lecture on skein valued open Gromov-Witten invariants and cluster mutations presented by Mingyuan Hu from Northwestern University at the M-Seminar, Kansas State University. Delve into the study of Lagrangians in \mathbb{C}^3 and their Ekholm-Shende wavefunctions, which encode open Gromov-Witten invariants across all genera and with varying numbers of boundary components. Discover the development of a skein valued cluster theory for computing these wavefunctions, with a focus on the Aganagic-Vafa brane case and its alignment with topological vertex predictions. Learn about the newly defined skein-valued dilogarithm and its proven pentagon relation, which has implications for the 5-term relation of Garsia and Mellit. Based on collaborative research presented in arXiv:2312.10186 and arXiv:2401.10817, this 1-hour 21-minute talk offers an in-depth exploration of cutting-edge mathematical concepts in algebraic geometry and topology.
