Seminarium KMMF "Teoria Dwoistości"

The neat algebraic reformulation of Feynman's heuristic path-integraldescription of quantum correlators in the framework of TopologicalQuantum Field Theory, due to Segal, Atiyah et al., has led to the discoveryof a plethora of topological invariants generalising the celebrated Jonespolynomial, but also - more recently - to a full-fledged proposal for aquantum (Rational) Conformal Field Theory.In this talk, we shall present Turaev's axiomatics of TQFT, discuss itsbasic implications, and sketch the fundamental application in asystematic construction of topological invariants of three-dimensionalmanifolds, based on the concept of a modular category. Time permitting,we shall also indicate the beautiful (and intrinsically geometric) relationbetween the latter TQFT and (a class of) two-dimensional CFTs.