Vaughan Jones University of California at Berkeley Date and time: Mon, 04/12/2004 - 4:00pm Physics, Room 202 Cantrell Lectures Monday, April 12, 2004 4:00p.m., Physics Bldg., Room 202 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. Tuesday, April 13, 2004 4:00p.m., Boyd Graduate Studies, Room 328 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. Wednesday, April 14, 2004 4:00p.m., Boyd Graduate Studies, Room 328 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.