Research Seminars @ Illinois

The walking adjunction is a 2-category corepresenting adjunctions. Remarkably, when we impose a "sphericality" condition on adjunctions, the resulting 2-category has a dual description in terms of algebraic geometry. This is the simplest equivalence in the conjectural "homological 3d mirror symmetry" program, originating from relative Langlands duality, which aims to give spectral decompositions of 2-categories arising from complex topology. We will give an introduction to this program, and its connections to representation theory and symplectic geometry.