Towards 2-Categorical 3D Mirror Symmetry

Explore the intricate connections between geometry, representation theory, and mirror symmetry in 3d N=4 supersymmetric quantum field theories through this advanced mathematics seminar. Delve into the study of hyper-Kähler manifolds equipped with hyper-Hamiltonian actions of compact Lie groups and their associated topological twists. Examine the 3d B-model (Rozansky-Witten theory) and the more enigmatic 3d A-model (3d Seiberg-Witten theory), focusing on their 2-categories of boundary conditions. Investigate the expected categorifications of category O for hyperkähler quotients and the potential categorification of Koszul duality between categories O for mirror symplectic resolutions. Learn about ongoing research in abelian gauge theories and how it extends previous work on pure gauge theory. Gain insights into cutting-edge mathematical concepts at the intersection of algebraic geometry, symplectic topology, and quantum field theory.