29/01/2003, 11:00 — 12:00 — Room P3.10, Mathematics Building Gonçalo Rodrigues, Instituto Superior Técnico
QFT's and state-sum models
Topological Quantum Field Theories (TQFT's) are a toy model for a
full blown theory of quantum gravity, associating in a functorial
way linear spaces to manifolds of dimension n and linear maps to
cobordisms. After a few definitions we go about their actual
construction via state sum models, focusing on the 1 + 1 situation,
conceptually and technically simpler although relatively
uninteresting, making reference to how one can extend the
constructions to higher dimensions. Along the way we will talk
about some work of the author on a particular extension of TQFT's,
Homotopical Quantum Field THeories (HQFT's) which can be seen as a
toy model of quantum gravity coupled to matter.
