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This is the webpage for a working seminar on Coulomb Branch Varieties. The first edition happened in autumn/winter 2019/20. As of July 2020, the seminar is now asynchronous, so it can be attended virtually at any time. The live talks have been replaced with a set of notes on Overleaf - each 'speaker' now adds a section to the notes for their 'talk'. The plan is for new 'talks' to be added about once a fortnight. The notes should also double as a discussion board - all participants are encouraged to add frequent questions and comments to the notes (which have some special LaTeX commands to make this easier).

A read-only version of the notes can be found here. To obtain a read/write link (which is essential to ask questions), please email Dougal Davis dougal.davis@ed.ac.uk. Also email Dougal to sign up for email updates.

Suggested talks: (Please volunteer!)

(Online!) Overview of Coulomb branch varieties (Dougal)

(Online!) Definition, toy examples and basic properties of Coulomb branch varieties, I (Dougal)

(Online!) Definition, toy examples and basic properties of Coulomb branch varieties, II (Dougal)

Braverman-Finkelberg, Coulomb branches of 3-dimensional gauge theories and related structures.
Braverman-Finkelberg-Nakajima, Towards a mathematical definition of Coulomb branches of 3-dimensional N = 4 gauge theories, II
Nakajima, Introduction to a provisional mathematical definition of Coulomb branches of 3-dimensional N = 4 gauge theories
Nakajima, Towards a mathematical definition of Coulomb branches of 3-dimensional N =4 gauge theories, I
Nakajima, Questions on provisional Coulomb branches of 3-dimensional N = 4 gauge theories.

More sophisticated examples (???)

Braverman-Finkelberg-Nakajima, Coulomb branches of 3d N = 4 quiver gauge theories and slices in the affine Grassmannian
Bezrukavnikov-Finkelberg-Mirkovic, Equivariant homology and K-theory of affine Grassmannians and Toda lattices

BFN resolutions and deformations (???)

Braverman-Finkelberg-Nakajima, Towards a mathematical definition of Coulomb branches of 3-dimensional N = 4 gauge theories, II, sections 3(vii)-(ix)
Weekes, Quiver gauge theories and symplectic singularities

Symplectic duality and Koszul duality (???)

Bernstein-Ginzburg-Soergel, Koszul Duality Patterns in Representation Theory.
Braden-Licata-Proudfoot-Webster, Quantizations of conical symplectic resolutions II: category O and symplectic duality.

Can someone do any physics about what underlies this (???)

Seiberg and Witten, Gauge Dynamics And Compactification To Three Dimensions
Bullimore, Dimofte, and Gaiotto, The Coulomb Branch of 3d N = 4 Theories
Bullimore, Dimofte, Gaiotto, and Hilburn, Boundaries, Mirror Symmetry, and Symplectic Duality in 3d N=4 Gauge Theory
Bullimore, Ferrari, and Kim, Twisted Indices of 3d N = 4 Gauge Theories and Enumerative Geometry of Quasi-Maps

Representation theory of Coulomb branch algebras (???)

Hilburn, Kamnitzer, and Weekes, BFN Springer theory

Page last modified on Thursday July 9, 2020 07:47:04 UTC