Workshop on Operator Algebras and Physics

There is a workshop on operator algebras and physics at the University of Cardiff, 21-25 June inclusive.

Operator algebras have their conception in quantum physics. The states of a quantum particle are understood as vectors in a Hilbert space. As all vector space of a given dimension are essentially the same one cannot really extract information about the system from the vector space structure. The important thing here is the algebra of operators on the Hilbert space. These do contain useful information.

For physics and noncommutative geometry C^{*} and von Neumann algebras are important, as are more general Banach algebras.

I am no expert on operator algebras, but I am interested in there use in physics and geometry. I need to brush up on them!

Constantin Teleman will be delivering a series of lectures on the five days on Two Dimensional Topological Quantum Field Theories and Gauge theories as part of the workshop. The interest in two dimensional theories comes largely from string theory and statistical physics. Also, systems in two dimensions can be thought of “toy models” for more realistic 4-d theories. There are some nice mathematical properties of low dimensional systems that allow one to get at features of quantum field theory that are hidden behind the difficulties encountered in higher dimensions.

A good place to start reading about these things is the preprint by Teleman “Topological field theories in 2 dimensions”; it can be found here as a pdf.

There are other good speakers giving talks.

I will write some kind of overview after the event.

Random thoughts on mathematics, physics and more…