Homological Mirror Symmetry - Introduction to 3D Mirror Symmetry

Explore the intricacies of 3d mirror symmetry in this hour-long lecture by Benjamin Gammage from Harvard University. Delve into a new formulation of the theory, focusing on the duality between holomorphic symplectic manifolds with Hamiltonian group actions. Examine the proposed equivalence between dual pairs of 2-categories (A- and B-type), which categorifies the A- and B-brane categories of homological (2d) mirror symmetry. Investigate the 2-categorical equivalence in the abelian case, including its implications for the spectral decomposition of the 2-category of spherical functors. Gain insights from Gammage's collaborative work with Justin Hilburn and Aaron Mazel-Gee in this advanced exploration of mirror symmetry theory.