Algebra and Logic Seminar - 12/3/2014

Wednesday, 12 March 2014, 2:00 p.m.

Lecturer: John Huerta (CAMGSD/IST-UL)

Title: "What can higher categories do for physics?"

Local: Room 1.4, Edifício VII
Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: We describe Baez and Dolan's cobordism hypothesis - a deep connection between topological quantum field theory, highercategories, and manifolds. Physically, the use of cobordisms encodes the idea that quantum field theories, even "topological" ones, should be local: no matter how we cut up the spacetime on which they are defined in order to perform the path integral, the net result must be the same. Recently, this hypothesis was formulated and proved by Jacob Lurie using the tools of homotopy theory. We describe the version of the hypothesis he proved. Finally, we touch on Freed, Hopkins, Lurie and Teleman's more recent work using the cobordism hypothesis to construct Chern-Simons theory with gauge group a torus.