Abstract: A vertex algebra is the chiral algebra of a two-dimensional conformal field theory and appears in many exciting problems. W-algebras are the broadest class of these and they are associated to certain data of Lie superalgebras. These W-algebras and their representation categories appear as invariants of 4-dimensional gauge theories and dualities of physics translate into isomorphisms of vertex algebras … Read More
Abstract: It has long been known that holomorphic field theories on twistor space lead to “physical” field theories on Minkowski space. In this talk I will discuss a type I (unoriented) version of the topological B model on twistor space. The corresponding theory on Minkowski space is a sigma-model with target the group SO(8). This is a variant of the … Read More
Abstract: Abelianization of flat connections is a construction motivated by supersymmetric quantum field theory, which has turned out to be connected to various bits of geometry — in particular, to Donaldson-Thomas theory, cluster algebra, the exact WKB method for analysis of ODEs, and hyperkahler geometry. In some of these subjects it is known that there exists a natural q-deformation which … Read More
Abstract: Integrable models are known to keep reemerging over time in various mathematical incarnations. Recently, such models based on quantum groups naturally appeared in the framework of enumerative geometry. In this context the so-called Bethe ansatz equations, instrumental for finding the spectrum of the XXZ model Hamiltonian, naturally show up as constraints for the quantum K-theory ring of quiver varieties. … Read More
Many problems in mathematical physics, from the WKB method to knot theory, involve quantum versions of algebraic curves. In this talk I will review an approach to the quantization of local mirror curves which makes it possible to reconstruct topological string theory on toric Calabi-Yau manifolds. In this approach, the quantization of the mirror curve leads to a trace class … Read More
Abstract: Braverman, Finkelberg, and Nakajima define the K-theoretic Coulomb branch of a 3d \mathcal N=4 SUSY gauge theory as the affine variety \mathcal M_{G,N} arising as the equivariant K-theory of certain moduli space \mathscr 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 … Read More
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
Abstract: I will explain a physically motivated construction of Ricci-flat K3 metrics via a hyper-Kähler quotient, which yields the first examples of explicit Ricci-flat metrics on compact non-toroidal Calabi-Yau manifolds. I will also relate it — both physically and mathematically — to a second such construction, which is as yet not completely explicit: the missing data is the BPS index … Read More