Professor Wenzl will continue his previous research using braid groups to construct interesting examples of subfactors of certain factors of von Neumann algebras. The following points will be emphasized: (a) It is planned to find a simpler and more conceptual approach to these examples using the theory of quantum groups more explicitly. Moreover, the braid groups will be used to construct other interesting subfactors. (b) Quantum groups also played an important role in the proof of the existence of certain invariants of 3-manifolds. Professor Wenzl plans to extend the approach used in this construction to treat not only the quantized Lie algebra of the special linear group in two dimensions, but all the classical Lie algebras. Professor Wenzl's research is in the area of self-adjoint operator algebras. These are families of operators (infinite dimensional matrices) with a certain reality condition imposed to make the algebras self-adjoint. Recent discoveries involving how one of these algebras sits inside another have brought together a bewildering variety of fields and have added immeasurably to our knowledge about these fields. Professor Wenzl's project will contribute to these developments.
