Conférencier: Joel Kamnitzer, University of Toronto
Résumé / Abstract:Conical symplectic resolutions often come in dual pairs. For example, the resolution of the type A_n singularity is dual to the cotangent bundle of projective space. One motivation for this duality comes from 3-dimensional quantum field theory, where these dual pairs are called the Higgs and Coulomb branches.
The Hikita conjecture relates the cohomology of one resolution to the coordinate ring of the other. Recently, two extensions of this conjecture have been proposed: an equivariant version (due to Nakajima) and a quantum version (due to McBreen, Proudfoot, and myself). I will describe these different conjectures and survey the recent progress towards their proofs.