Andrei Negut (MIT) “q-deformed W-algebras, Ext operators and the AGT-W relations”
ABSTRACT: I will present a construction of the q-deformed W-algebra of gl_r and its Verma module, that does not use the free field realization or screening charges. The upshot is that our method allows us to directly compute the commutation relations between the Carlsson-Okounkov Ext operator on the moduli space of rank r sheaves and the defining currents of the … Read More
Dmitry Galakhov (UCB) “The Two-Dimensional Landau-Ginzburg Approach To Link Homology”
ABSTRACT: We describe rules for computing a homology theory of knots and links in R^3. It is derived from the theory of framed BPS states bound to domain walls separating two-dimensional Landau-Ginzburg models with (2,2) supersymmetry. We illustrate the rules with some sample computations, obtaining results consistent with Khovanov homology. We show that of the two Landau-Ginzburg models discussed in … Read More
Lotte Hollands (Heriot-Watt University) “Opers, spectral networks and the T[3] theory”
ABSTRACT: In this seminar I will explain how certain partition functions of four-dimensional quantum field theories, such as the non-Lagrangian T[3] theory, have a geometric interpretation as generating functions of so-called opers. This will reveal close ties to spectral networks and the exact WKB method. (This is joint work with Andy Neitzke.)
Michael Viscardi (UCB) “Equivariant quantum cohomology and the geometric Satake equivalence”
ABSTRACT: Recent work on equivariant aspects of mirror symmetry has discovered relations between the equivariant quantum cohomology of symplectic resolutions and Casimir-type connections (among many other objects). We provide a new example of this theory in the setting of the affine Grassmannian, a fundamental space in the geometric Langlands program. More precisely, we identify the equivariant quantum connection of certain … Read More
Pavel Putrov (IAS) “Resurgence in Chern-Simons theory”
ABSTRACT: In my talk I will consider resurgence properties of Chern-Simons theory on compact 3-manifolds. I will also describe what role resurgence plays in the problem of categorification of Chern-Simons theory, that is the problem of generalizing Khovanov homology of knots to compact 3-manifolds.
NOTICE UNUSUAL TIME! Nikita Nekrasov (Stony Brook University) “How I learned to stop worrying and to love both instantons and anti-instantons”
ABSTRACT: In quantizing classical mechanical systems to get (non-perturbative in hbar corrections to) the eigenvalues of the Hamiltonian one often sums over the classical trajectories as in localisation formulas, but also take into account the contributions of the so-called “instanton-antiinstanton gas”. The latter is an ill-defined set of approximate solutions of equations of motion. The talk will attempt to alleviate … Read More
Andrey Smirnov (UCB) “Quantum K-theory and Nekrasov-Shatashvili conjecture”
ABSTRACT: In my talk I will discuss the construction of quantum K-theory using the moduli spaces of quasimaps. This construction works well for Nakajima quiver varieties and I will illustrate it on the simplest example: the cotangent bundles over grassmannians.