Abstract: The category of finite dimensional sl(2) representations admits a combinatorial description in terms of Temperley-Lieb diagrammatics.  In this talk I will introduce a “dotted” version of the Temperley-Lieb graphical calculus and show that it describes two categories of interest in representation theory and topology: (1) the category of coherent sheaves on the sl(2) nilpotent cone and (2) the annular Bar-Natan category (this latter category appears in the context of Khovanov homology for links in a thickened annulus). There is a highest weight structure on the derived category of the nilpotent cone, in which the (co)standard objects are given by Bezrukavnikov’s quasi-exceptional objects, and the connection with the annular Khovanov invariant enables us to give an elegant description in terms of some special annular links. This is based on recent joint work with Dave Rose and Paul Wedrich. 

12:15pm, 511 Lake Hall,  Matt Hogancamp (Northeastern University)