## Quantum Topology / Hopf Algebra Seminar

James Otto

UIC

Operator Topologies, * Algebras, and Conditional Expectations

**Abstract:**We note a goodness/badness (separable, metrizable, Baire, ... ) dance for operator topologies and how group algebras and towers of finite dimensional algebras close up under these topologies to AF C* algebras and hyperfinite W* algebras. We relate commutative * algebras to topology and measure theory and non-commutative * algebras to quantum theory. We indicate the passage from subalgebras to conditional expectations to Temperley-Lieb algebras.

Tuesday December 5, 2017 at 3:00 PM in SEO 612