Abstract: 

A classical theorem of Jones says that one can obtain the HOMFLY polynomial from the Markov trace on the Hecke algebra. Khovanov categorified this construction using Ext groups between Soergel Bimodules to produce (triply graded) link homology. In this talk, we introduce a diagrammatic framework for studying (in rank 2) Ext Enhanced Soergel Bimodules, a full monoidal subcategory of D^b(R-Bimodules), where R is a polynomial ring. This construction provides a novel approach to computations in the derived category, circumventing the usual technical challenges associated with chain maps, chain homotopies, quasi-isomorphisms, and Ext groups. As an application, we present new computations in (triply graded) link homology that hold uniformly for any positive or negative link.

Li Chun Chun, Academia Sinica, Postdoc