Abstract: In the first part of the talk, I will recall Kazhdan-Lusztig’s geometric realization of the affine Hecke algebra H_q as well as Bezrukavnikov’s categorification of the statement. One of the fundamental tools of the theory is the so-called asymptotic affine Hecke algebra introduced by Lusztig (it can be thought of as a “limit” of H_q as “q goes to … Read More
Abstract: To each compact, orientable surface S whose connected components have non-empty boundary, we define a dg category whose objects are neatly embedded 1-manifolds in S. In the case when S is a disk, this recovers the so-called “Bar-Natan category”: the natural setting for Khovanov’s celebrated categorification of the Jones polynomial. We expect that these dg categories form part of the … Read More
ABSTRACT: Given a Riemann surface C and a central charge c, one can define the notion of Virasoro conformal block. Virasoro conformal blocks capture universal features of conformal field theory on C. I will describe a new scheme for constructing Virasoro conformal blocks at central charge c=1, by relating them to simpler “abelian” objects, namely conformal blocks for the Heisenberg … Read More
Abstract: Many interesting varieties can be realized as the Coulomb branch of a 3d N=4 gauge theory, and this realization can give us some very interesting information. One of the most familiar varieties that appears this way is the cotangent bundle of the Grassmannian of k-planes in C^n. I’ll explain this realization as a special case of the more general … Read More
Abstract: In this talk I will start with introducing a new presentation of deformed double current algebra of type gl_k, denoted by A^{(k)}, which is motivated from the study of M2 branes in the twisted M-theory. Then I will explain how to find an algebra embedding from A^{(k)} to the mode algebra of W^{(k)}_\infty, which is a matrix-extended generalization of … Read More