{"id":220,"date":"2023-11-09T11:08:03","date_gmt":"2023-11-09T11:08:03","guid":{"rendered":"https:\/\/hodge.maths.ed.ac.uk\/?page_id=220"},"modified":"2023-11-09T11:08:03","modified_gmt":"2023-11-09T11:08:03","slug":"coulomb-branch-varieties","status":"publish","type":"page","link":"https:\/\/hodge.maths.ed.ac.uk\/?page_id=220","title":{"rendered":"Coulomb Branch Varieties"},"content":{"rendered":"\n

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<\/strong>, 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).<\/p>\n\n\n\n

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

Suggested talks: (Please volunteer!)<\/p>\n\n\n\n

(Online!) Overview of Coulomb branch varieties<\/strong> (Dougal)<\/p>\n\n\n\n

(Online!) Definition, toy examples and basic properties of Coulomb branch varieties, I<\/strong> (Dougal)<\/p>\n\n\n\n

(Online!) Definition, toy examples and basic properties of Coulomb branch varieties, II<\/strong> (Dougal)<\/p>\n\n\n\n

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

More sophisticated examples<\/strong> (???)<\/p>\n\n\n\n

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

BFN resolutions and deformations<\/strong> (???)<\/p>\n\n\n\n

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

Symplectic duality and Koszul duality<\/strong> (???)<\/p>\n\n\n\n

Bernstein-Ginzburg-Soergel, Koszul Duality Patterns in Representation Theory<\/a>.
Braden-Licata-Proudfoot-Webster, Quantizations of conical symplectic resolutions II: category O and symplectic duality.<\/a><\/p>\n\n\n\n

Can someone do any physics about what underlies this<\/strong> (???)<\/p>\n\n\n\n

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

Representation theory of Coulomb branch algebras<\/strong> (???)<\/p>\n\n\n\n

Hilburn, Kamnitzer, and Weekes, BFN Springer theory<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

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 […]<\/p>\n","protected":false},"author":1,"featured_media":76,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-220","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages\/220","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=220"}],"version-history":[{"count":1,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages\/220\/revisions"}],"predecessor-version":[{"id":221,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages\/220\/revisions\/221"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/media\/76"}],"wp:attachment":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}