Speaker
Description
According the cobordism hypothesis (proposed by Baez-Dolan, and proved by Lurie), an extended topological quantum field theory is fully determined by its value on the point. A natural question is then: does this classification theorem apply to the topological quantum field theories of physical interest? And if yes, what is then the value of those theories on a point (the latter will then determine the whole theory, by the cobordism hypothesis). In this talk, we will propose answers to the questions “What does Chern-Simons theory assign to a point?” and “What kind of mathematical object does Chern-Simons theory assign to a point?” The answer to the first question is "representations of the based loop group"; the answer to the second question is "categorified von Neumann algebras".
