Statut  Confirmé 
Série  SEMDARBOUX 
Domaines  hepth,math.AG 
Date  Jeudi 15 Décembre 2022 
Heure  11:00 
Institut  LPTHE 
Salle  bibliothèque du LPTHE, tour 1314, 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 ominimality 
Résumé  I will give a gentle introduction to some recent applications of ominimal 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 ominimal 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 ominimal 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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