Research

My research is on various aspects of the interaction between representation theory, quantum field theory, algebraic geometry and topology.

A central theme is the construction of symplectic singularities and their quantizations from supersymmetric gauge theories in three dimensions. Most notably, these theories exhibit 3-dimensional mirror symmetry, a duality that (in particular) exchanges the Higgs branch of one theory with the Coulomb branch of its mirror. You can learn more about this in my recent survey article.

On the mathematical side, I study the geometry and algebra of these spaces—especially Coulomb branches as introduced by Braverman-Finkelberg-Nakajima—and their representation theory. This includes connections to Cherednik algebras, quantum groups, and various flavors of categorification.