Abstract: One of the great surprises to emerge from string theory is the prediction of supersymmetric QFTs with interacting UV superconformal fixed points in 5d and 6d. Although 6d superconformal fixed points are believed classified, the classification of 5d superconformal fixed points remains an open problem. In this talk, I discuss recent progress towards a classification of 5d fixed points … Read More
Abstract: A special case of the geometric Langlands correspondence is given by the relationship between solutions of the Bethe ansatz equations for the Gaudin model and opers – connections on the projective line with extra structure. In this paper, we describe a deformation of this correspondence for SL(N). We introduce a difference equation version of opers called q-opers and prove … Read More
ABSTRACT: I will present the rank N magnificent four theory, which is the supersymmetric localization of U(N) super-Yang-Mills theory with matter on a Calabi-Yau fourfold, and conjecture an explicit formula for the partition function Z: it has a free-field representation, and surprisingly it depends on Coulomb and mass parameters in a simple way. Based on joint work with N.Nekrasov.
A classical result of Turaev identifies the skein algebra of the annulus with the algebra of symmetric functions in infinitely many variables. Queffelec and Roze categorified this using annular webs and foams. I will recall their construction and compute explicit symmetric functions and their categorical analogues for some links. As an application, I will describe spectral sequences computing categorical invariants … Read More
Abstract: Virasoro constraints are omnipresent in enumerative geometry. Recently, Kontsevich and Soibelman introduced a generalization of Virasoro constraints in the form of Airy structures. It can also be understood as an abstract framework underlying the topological recursion of Chekhov, Eynard and Orantin. In this talk I will explain how the triumvirate of Virasoro constraints, Airy structures and topological recursion can … Read More
Abstract: Calabi-Yau manifolds have played a central role in both string theory and mathematics for decades, but in spite of this no Ricci-flat metric on a compact non-toroidal Calabi-Yau manifold is known. I will discuss a new physically motivated approach toward the determination of such metrics for K3 surfaces. The key remaining step is the determination of a BPS spectrum … Read More
This is a joint work with A. Oblomkov exploring the relation between the HOMFLY-PT link homology and coherent sheaves over the Hilbert scheme of points on C^2. We consider a special object in the 2-category related to the Hilbert scheme of n points on C^2. We define a homomorphism from the braid group on n strands to the monoidal category … Read More
Abstract: I will describe joint work with Ciprian Manolescu on constructing an analogue of instanton Floer homology replacing the group SU(2) by SL(2,C). Having failed to do so using the standard Floer theoretic tools of gauge theory and symplectic topology, we turned to sheaf theory to produce an invariant. After describing our approach, I will discuss some features of this … Read More
Basing on the representation theory of quantum toroidal algebras we propose a generalization of the refined topological vertex formalism incorporating additional “Higgsed” vertices and lines apparently corresponding to refined Lagrangian branes. We find rich algebraic structure associated to brane diagrams incorporating the new vertices and lines. In particular, we build the screening charges associated to W-algebras of types gl(n) and … Read More
Abstract: 3 dimensional N=4 supersymmetric quantum field theories have two distinguished topological twists, called Higgs and Coulomb (though we periodically get confused about which is which). These two twists manifest very interesting mathematical objects in Lie theory and algebraic geometry, which don’t seem to obviously be related, except through this bridge in QFT. I’ll do my best to explain what … Read More