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Representation theory and the Coulomb branch

Presented by: 
Ben Webster University of Virginia
Tuesday 27th June 2017 - 14:30 to 15:30
INI Seminar Room 1
For many years, my collaborators and I tried to understand the Coulomb branches of certain field theories from physics and failed miserably. Luckily, recent work of Braverman-Finkelberg-Nakajima gives a mathematical construction of these spaces, and algebras quantizing them. I'll discuss an approach to the representation theory of these algebras (building on joint work with Braden-Licata-Proudfoot and many other authors). Applications include a version of the Koszul duality between the Higgs and Coulomb branches of such a theory, a new perspective on category O for Cherednik algebras, and a new understanding of coherent sheaves on Coulomb branches in terms of KLR algebras.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons