Mathematics Colloquia and Seminars

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For a hypertoric variety T, Kuwabara constructed a sheaf of vertex algebras on T that is locally isomorphic to the Chiral-de-Rham complex of T. This sheaf of VOA is in essence the boundary VOA of Costello-Gaiotto for the A twist of 3d N=4 theory with target T, whose representation theory is the central theme of my joint work to appear with A. Ballin, T. Creutzig and T. Dimofte (BCDN). In this talk, I will explain work in progress of constructing a sheaf of VOA on T based on the shifted tangent complex of T, a construction inspired by 3d mirror symmetry of boundary VOA. I will show that localization of this sheaf of VOA leads to interesting tensor functors between braided tensor category of VOA modules.