Seminario di Geometria e Analisi Complessa: Geometric realisations of Lie superalgebras

Il Prof. Jose' Figueroa-O'Farrill, della School of Mathematics dell'Università di Edinburgo, terra' una serie di lezioni dal titolo "Geometric realisations of Lie superalgebras" nei giorni giovedì 24 e venerdì 25 maggio 2007, dalle ore 15.00 alle ore 16.45, nell'aula seminari "F. Tricerri" del Dipartimento di Matematica "U.Dini" di Firenze .

Abstract: It is well-known that many Lie algebras can be interpreted as the Lie algebra of vector fields on a manifold preserving some structure: a metric, a symplectic form,... In these talks I'd like to introduce a similar realisation of Lie superalgebras as 'supersymmetries' of 'supergravity backgrounds'. The talk will not presuppose any previous knowledge of physics. A 'supergravity background' will be defined in terms of geometric structures on a manifold satisfying certain natural PDEs and 'supersymmetries' as spinor fields satisfying some differential/algebraic equations. From this data I will show that one can construct naturally a Lie superalgebra and give plenty of examples. If time allows, I will describe some uses of this construction in finding new supergravity backgrounds.