Presentations

Coulomb branches and representation theory, at Canada-Mexico-USA Conference in Representation Theory, Noncommutative Algebra, and Categorification, Northeastern University, Boston, Sunday, June 12, 2022:
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
Noncommutative resolutions of Coulomb branches Monday, October 25, 2021

video of the talk  slides for the talk

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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Knot homology and coherent sheaves on Coulomb branches Thursday, April 8, 2021

video of the talk slides for the talk

Recent work of Aganagic proposes the construction of a homological knot invariant categorifying the Reshetikhin-Turaev invariants of miniscule representations of type ADE Lie algebras, using the geometry and physics of coherent sheaves on a space which one can alternately describe as a resolved slice in the affine Grassmannian, a space of G-monopoles with specified...

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Hypertoric mirror symmetry Thursday, November 5, 2020:

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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Coulomb branches and cylindrical KLRW algebras Friday, September 11, 2020:

video of the talk: part I

video of the talk: part II

Abstract:  Remarkable work of Braverman-Finkelberg-Nakajima has constructed, based on some fancy quantum field theory, a fascinating collection of spaces called "Coulomb branches." The definition of these involves the geometry of affine Grassmannians, and thus is not so easy for many people think about.  Luckily, the algebraic tools for understanding the most...

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