Symplectic duality in examples

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 TQFTs and, therefore, fall within the framework of 3D mirror symmetry, also known as symplectic duality. The first part of the talk will provide a gentle introduction to the theory of symplectic singularities, with an emphasis on various examples. In the second part, we will discuss how the symplectic duality works in examples, beginning with the simplest cases. We will then discuss a particular phenomenon called the Hikita-Nakajima conjecture, which predicts a deep and nontrivial relationship between dual varieties. It is particularly intriguing that this conjecture was formulated by mathematicians and still requires further understanding from a physical perspective.