Knots and polynomials
Abstract: We will describe certain invariants of knots in three dimensional space and give an impressionistic view of how they relate to physics, algebra and analysis. The notion of subfactor will be introduced.
The analytic and algebraic flavours of subfactors
Abstract: Subfactors are algebras of operators on Hilbert space, so their properties rely on results from analysis. On the other hand they have field-like properties that make it desirable to treat them like Galois theory. The analysis and the algebra go hand in hand.
Subfactors and Physics
Abstract: The state space of the quantum world is defined by a Hilbert space. Observables are operators on that Hilbert space. Thus it is not surprising that subfactors occur in quantum physics. We will present a few instances of this, including a speculative use of the Connes tensor product for combining two quantum systems.
*Refreshments will be served at 3:30p.m., preceding each lecture.