Explore equivariant Fukaya categories and their relation to Hamiltonian reductions in this lecture by Yanki Lekili from Imperial College London. Delve into new conjectures and examples connecting wrapped Fukaya categories of symplectic manifolds with Hamiltonian S^1 actions to their Hamiltonian reductions. Examine topics such as Korean comology, simplexic topology, and mirror algebraic variety. Investigate key observations, general conjectures, and surprising elements in the field. Learn about invertible elements, lambda components, and sympathetic reduction. Analyze the concepts of regular value, C tier structure, and relative category. Gain insights from this joint work with Ed Segal, presented at the M-Seminar at Kansas State University.