Braverman, Finkelberg, and Nakajima define the K-theoretic Coulomb branch of a 3d N=4 SUSY gauge theory as the affine variety M_{G,N} arising as the equivariant K-theory of certain moduli space R_{G,N}, labelled by the complex reductive group G and its complex representation N. It was conjectured by Gaiotto, that (quantized) K-theoretic Coulomb branches bear the structure of (quantum) cluster varieties. … Read More

The 4D/2D correspondence recently discovered by Beem et al. constructs representation theoretical objects, such as representations of affine Kac-Moody algebras, as invariants of 4 dimensional superconformal field theories with N = 2 supersymmetry. Furthermore, it is expected that there is a remarkable duality between the representation theoretical objects constructed in this way and the geometric invariants called Higgs branch of … Read More

Time: 1:10pm Abstract:We propose a geometric characterisation of the topological string partition functions associated to the local Calabi-Yau (CY) manifolds used in the geometric engineering of d = 4, N = 2 supersymmetric field theories of class S. A quantisation of these CY manifolds defines differential operators called quantum curves. The partition functions are extracted from the isomonodromic tau-functions associated … Read More