Abstract: A conjecture of Dunfield-Gukov-Rasmussen predicts a family of differentials on reduced HOMFLYPT homology, indexed by the integers, that give rise to a corresponding family of reduced link homologies. We’ll discuss a variant of this conjecture, constructing an unreduced link homology theory categorifying the quantum gl_n link invariant for all non-zero values of n (including negative values!). To do so, … Read More

ABSTRACT: A conjecture of Gorsky-Negut-Rasmussen asserts the existence of a pair of adjoint functors relating the Hecke category for symmetric groups and the Hilbert scheme of points in the plane. One topological consequence of this conjecture is the prediction of a deformation of the triply graded Khovanov-Rozansky link homology which restores the missing q—>tq^{-1} symmetry of KR homology for links. … Read More

ABSTRACT: I will describe a construction which, for a given 4D N=2 Argyres-Douglas SCFT, seems to produce a three-dimensional TQFT, whose underlying modular tensor category coincides with that of a 2d chiral algebra of the parent 4d N=2 theory.

ABSTRACT: We revisit Donaldson-Witten theory, that is the N=2 topologically twisted super Yang-Mills theory with gauge group SU(2) or SO(3) on compact 4-manifolds. We study the effective action in the Coulomb branch of the theory and by considering a specific Q-exact deformation to the theory we find interesting connections to mock modular forms. A specific operator of this theory computes … 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 Nikita Nekrasov.

Abstract: In my talk I will consider a quantum integrable Hamiltonian system with two generic complex parameters q,t whose classical phase space is the moduli space of flat SL(2,C) connections on a genus two surface. This system and its eigenfunctions provide genus two generalization of the trigonometric Ruijsenaars-Schneider model and Macdonald polynomials, respectively. I will show that the Mapping Class … Read More

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