Event Category: Berkeley String-Math Seminar

Berkeley String-Math Seminar

–

Abstract: I will explain how to define a t-structure on the wrapped Fukaya category of a complex conic symplectic manifold, whose heart is the global sections of a perverse sheaf of categories on the core of the symplectic manifold. Here, a perverse sheaf of a categories is just a sheaf of categories whose hom sheaves are (shifted) perverse. I will … Read More

–

Abstract: Many gauge theories in four dimensions are based on PDEs that involve a gauge connection coupled to other fields. The latter are usually a source of a major headache since they lead to non-compactness of the moduli spaces. Today we will discuss two aspects of this major problem and two ways of dealing with it. One will help us … Read More

–

Using brane quantization, we study the representation theory of the spherical double affine Hecke algebra of type in terms of the topological A-model on the moduli space of flat -connections on a once-punctured torus. In particular, we provide an explicit match between finite-dimensional representations and A-branes with compact support; one consequence is the discovery of new finite-dimensional indecomposable representations. We … Read More

–

Abstract:Homological mirror symmetry predicts an equivalence between the derived category of equivariant coherent sheaves on the additive Coulomb branch X and a version of the wrapped Fukaya category on multiplicative Coulomb branch Y with superpotential W. If one decategorifies both sides by taking K-theory, the construction still gives an interesting identification between well-known objects in the equivariant K-theory of X … Read More

–

Abstract: I will discuss algebraic structures associated to moduli of sheaves on elliptic surfaces, and describe their relation with other parts of mathematical physics. These algebraic structures control the enumerative geometry of these moduli spaces analogous to how quantum groups control enumerative invariants of quiver varieties. The main results discussed will include a description of the quantum differential equation in … Read More

–

In her recent work, Mina Aganagic proposed novel perspectives on computing knot homologies associated with any simple Lie algebra. One of her proposals relies on counting intersection points between Lagrangians in Landau-Ginsburg models on symmetric powers of Riemann surfaces. In my talk, I am going to present a concrete algebraic algorithm for finding such intersection points, turning the proposal into … Read More

–

Abstract: “I will report on a joint work in progress with Pablo BoixedaAlvarez, Michael McBreen and Zhiwei Yun where categories of microlocal sheaves on some affine Springer fibers are described in terms of theLanglands dual group. In particular, in the slope 1 case we recover the regular block in the category of (graded) modules over the smallquantum groups. Assuming a general formalism … Read More

–

Abstract: In work to appear with Ballin-Creutzig-Dimofte, we constructed vertex operator algebras associated to A and B twists of 3d N=4 abelian gauge theories. These are boundary VOAs supported on holomorphic boundary conditions of Costello-Gaiotto. For the B twist, the vertex algebra V_B is a simple current extension of an affine Lie superalgebra, and using the work of Creutzig-Kanade-McRae, we … Read More

–

In a landmark work, Frances Kirwan described the relation between the cohomology of a GIT quotient of a smooth projective variety X and the equivariant cohomology of X by what is known as the ‘subtraction method’: this relies on the equivariant perfection of the destabilizing stratification of X. Later work geared toward describing the cohomology ring structure relied on Poincare … Read More