Coulomb branches of quiver gauge theories are a type of almost commutative algebra arising from 3d quantum field theory.  These include many popular algebras, like universal enveloping algebras, W-algebras and Cherednik algebras of type A.  Realizing these algebras as Coulomb branches emphasizes the role of a commutative subalgebra (generalizing the Gelfand-Tsetlin subalgebra of the universal enveloping algebra), and analyzing the representation theory of these algebras with respect to these commutative subalgebras naturally gives rise to flavoured KLRW algebras.  I'll try to... Read more about Coulomb branches and representation theory

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Given a 3d N=4 supersymmetric quantum field theory, there is an associated Coulomb branch, which is an important reflection of the A-twist of this theory. In the case of gauge theories, this Coulomb branch has a description due to Braverman-Finkelberg-Nakajima; I'll discuss how we can generalize this geometric description in order to construct non-commutative resolutions of Coulomb branches (giving a more...

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video of the talk

I’ve frequently heard the assertion that “hyperkahler manifolds are self-mirror up to rotation.” I’m not so sure this is true in general, but I know one example of such a variety:  multiplicative hypertoric varieties; these are what happens when you cut up a real torus into polytopes, and then send the polytopes to have a toric hyperkahler party.  I’ll discuss recent work with Gammage and McBreen showing that self-homological homological mirror symmetry after rotation...

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