Symplectic singularities were introduced by Beauville in the beginning of 2000's. Many of such varieties appear in representation theory as well, in particular, their quantizations are often algebras with interesting representation theory. The most famous example is the universal enveloping algebras of semisimple Lie algebras.

In this talk, I will explain that the “chiral” quantizations of symplectic singularities also appear in connection with 4 dimensional N=2 supercomformal field theories in physics.