Event Category: Berkeley String-Math Seminar

Berkeley String-Math Seminar

–

While the BPS state counting problem in general toric Calabi-Yau manifolds was solved a decade ago, it has long remained an unsolved problem to identify the underlying BPS state algebra. Recently, we solved this problem by introducing a new infinite-dimensional algebra, the BPS quiver Yangian. We constructed representations of the algebra in terms of crystal melting, and derived the representations … Read More

–

It is a general expectation that the refined topological string theory of local Calabi-Yau 3-folds produces quasimodular forms which are solutions of some refined holomorphic anomaly equation. I will present a mathematical derivation that it is indeed the case for the refined topological string on local P^2 in the Nekrasov-Shatashvili limit. The rather indirect proof exploits mathematical incarnations of various … Read More

–

We analyze symmetries corresponding to separated topological sectors of 3d N= 4gauge theories with Higgs vacua, compactified on a circle. The symmetries are encoded in Schwinger-Dyson identities satisfied by correlation functions of a certain gauge-invariant operator, the “vortex character.” Such a character observable is realized as the vortex partition function of the 3d gauge theory, in the presence of a … Read More

–

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 to the … Read More

–

Abstract: Starting with some context and motivation from a mathematical and physical perspective, I will discuss recent work with Raphael Rouquier on a higher tensor product operation for 2-representations of Khovanov’s categorification of U(gl(1|1)^+), examples of such 2-representations that arise as strands algebras in bordered and cornered Heegaard Floer homology, and a tensor-product-based gluing formula for these 2-representations expanding on … Read More

–

Abstract: Stacks of M2-branes in Omega background lead to a class of Coulomb branch algebras due to Kodera and Nakajima. On the other hand, stacks of M5-branes in Omega background lead to a class of vertex operator algebras due to a version of the AGT correspondence. I will provide a new interpretation of key objects in the theory of vertex … Read More

–

Knizhnik-Zamolodchikov (KZ) equation was derived in late 1980s from Ward identities of two dimensional conformal field theory with a current algebra symmetry. It is obeyed by the WZNW conformal blocks but remarkably admits analytic continuation in spins, magnetic quantum numbers and the level. In this talk I will review the work of recent years in which this extension meets the … Read More

–

Abstract: Two-dimensional integrable field theories are characterised by the existence of infinitely many integrals of motion. Recently, two unifying frameworks for describing such theories have emerged, based on four-dimensional Chern-Simons theory in the presence of surface defects and on Gaudin models associated with affine Kac-Moody algebras. I will explain how these formalisms can be used to construct infinite families of … Read More