Geometry Seminar

Over the past twenty years, mathematicians and physicists have shown increasing interest in studying certain Poisson varieties, known as “symplectic singularities.” Many of these objects naturally arise as Higgs or Coulomb branches of certain 3D N=4 topological quantum field theories and, therefore, fall within the framework of 3D mirror symmetry, also known as symplectic duality. We will discuss how the symplectic duality works in examples, beginning with the simplest cases. We will then discuss a particular phenomenon called the (quantum) Hikita-Nakajima conjecture, which predicts a nontrivial relationship between dual varieties. Notably, it allows us to formulate concrete conjectures about one side of the duality by studying the other. Partially based on joint works with Hoang, Matvieievskyi, and Shlykov, and the work in progress with Dinkins and Karpov.