Operator Algebras Seminar, Winter 1997

• Date: 1/16/97 (Mathematics Colloquium)
  • Speaker: Sorin Popa, UCLA
  • Title: Amenability in the theory of subfactors
  • Abstract: Vaughan Jones proposed in the early 80's the study of inclusions of certain algebras of operators (or subfactors), which arise naturally as algebras of symmetries in quantum physics, and proved some suprising rigidity results. A rich theory has developed since then with many interesting and fruitful connections to other areas of mathematics (e.g. knot theory) and theoretical physics (e.g. conformal field theory). A subfactor can be viewed as a group like object and a variety of techniques and concepts extensively used in group theory have counterparts in the theory of subfactors and play a crucial role there. We will explain in this talk the concept of amenability in the theory of subfactors and we will show how it leads to profound theorems about the structure of subfactors. We will start with a discussion of the different descriptions of amenability for groups, such as Kesten's theorem, and show how it can be extended to operator algebras in a natural way.
• Date: 1/17/97
  • Speaker: Darren Long, UCSB
  • Title: The beginner's guide to the nonfaithfulness of the Burau representation

• Date: 1/24/97
  • no meeting this week (because of the MSRI workshop on Vassiliev invariants)

• Date: 1/31/97
  • Speaker: Raymond Lickorish, Cambridge University (visiting UCSB)
  • Title: Skein theory - How algebras occur in knot theory

• Date: 2/7/97
  • no meeting

• Date: 2/14/97
  • no meeting

• Date: 2/21/97
  • Speaker: Corran Webster, UCLA
  • Title: The Krein-Milman Theorem in Operator Convexity
  • Abstract: We generalize the Krein-Milman theorem to the setting of matrix convex sets of Effros-Winkler, extending the work of Farenick-Morenz on compact C*-convex sets of matrices and matrix state spaces of C*-algebras. (Joint work with Soren Winkler).

• Date: 2/28/97
  • Speaker: Teodor Banica, Universite de la Mediterranee, CNRS
  • Title: Some examples of compact quantum groups

• Date: 3/7/97
  • Speaker: Feng Xu, UCLA
  • Title: ``Exceptional'' subfactors and integrable models
  • Abstract: In this talk I will describe how various puzzles about exceptional subfactors and integrable lattice models can be resolved in the framework of constructive quantum field theory in two dimensions. The relation of such a theory to low-dimensional toplogy and quantum groups will also be briefly mentioned.