Symplectic duality and Hikita-Nakajima conjecture 
 
Abstract: 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 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 Hikita-Nakajima conjecture, which predicts a nontrivial relationship between dual varieties. Specifically, it describes the algebra of (equivariant) cohomology of one variety in terms of the geometry of the dual variety. Based on joint works with Hoang, Matvieievskyi and Shlykov.  

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