Statut  Confirmé 
Série  SEMDARBOUX 
Domaines  hepth 
Date  Lundi 30 Mars 2015 
Heure  16:30 
Institut  LPTHE 
Salle  bibliothèque du LPTHE 
Nom de l'orateur  Vlassopoulos 
Prenom de l'orateur  Yiannis 
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Titre  CalabiYau algebras and Topological Quantum Field Theories 
Résumé  A CalabiYau ($CY$) algebra is a differential graded (or more generally $A_\infty$) algebra with finite dimensional cohomology and a certain kind of duality. An example is the de Rham algebra of forms on a compact closed oriented manifold. Given a $CY$ algebra one can construct a 1+1 dimensional topological quantum field theory (TQFT). $CY$ algebras appear on both sides of the mirror symmetry conjecture for compact $CY$ manifolds, coming from string theory. We shall explain how to generalize $CY$ algebras to the case where the cohomology of the algebra is not necessarily finite dimensional and the duality condition is relaxed. Such algebras are called $preCY$ and examples include the de Rham algebra of forms on a manifold with boundary. We shall explain how to construct a 1+1 dimensional TQFT from a $preCY$ algebra, via acyclic directed ribbon graphs. $PreCY$ algebras appear on both sides of the mirror symmetry conjecture for open $CY$ manifolds and for Fano manifolds. This is joint work with Maxim Kontsevich. 
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