# Topological Quantum Field Theory Seminar

### Categorified $q$-Schur algebra and the BMW algebra

In 1989 François Jaeger showed that the the Kauffman polynomial of a link $L$ can be obtained as a weighted sum of HOMFLYPT polynomials on certain links associated to $L$. In this talk I will explain how to use a version of Jaeger's theorem to stablish a connection between the $\mathrm{SO}\left(2N\right)-\mathrm{BMW}$ and the $q$-Schur algebras. I will then present a subcategory of the Schur category which categorifies the $\mathrm{SO}\left(2N\right)-\mathrm{BMW}$ algebra (joint with E. Wagner).
Support: FCT, CAMGSD, New Geometry and Topology.. (Room P4.35 still to be confirmed)