Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Statut Confirmé
Domaines hep-th,math.AG
Date Jeudi 15 Décembre 2022
Heure 11:00
Institut LPTHE
Salle bibliothèque du LPTHE, tour 13-14, 4eme étage
Nom de l'orateur Fresan
Prenom de l'orateur Javier
Addresse email de l'orateur
Institution de l'orateur Ecole Polytechnique
Titre Hodge theory and o-minimality
Résumé I will give a gentle introduction to some recent applications of o-minimal techniques to questions in Hodge theory and functional transcendence, due to Bakker, Brunebarbe, Klingler, and Tsimerman. Roughly speaking, a structure is a collection of subsets of the power set of R^n, one for each n, that are definable by first order formulas involving the operations and the order coming from the real numbers, as well as function of a certain class chosen beforehand (e.g. the real exponential). Such a structure is called o-minimal if the subsets of R are finite unions of points and open intervals. This tameness condition allows one to develop topology or geometry without the usual pathologies that one encounters while working with arbitrary spaces. For example, if a closed subset of an analytic variety is definable in some o-minimal structure, then it is automatically algebraic, whether the ambient space is proper or not. I will explain why period maps coming from Hodge theory are definable in a suitable o- minimal structure, and a few spectacular consequences of this result.
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