Status  Confirmed 
Seminar Series  SEMDARBOUX 
Subjects  hepth,math.AG 
Date  Thursday 15 December 2022 
Time  11:00 
Institute  LPTHE 
Seminar Room  bibliothèque du LPTHE, tour 1314, 4eme étage 
Speaker's Last Name  Fresan 
Speaker's First Name  Javier 
Speaker's Email Address  
Speaker's Institution  Ecole Polytechnique 
Title  Hodge theory and ominimality 
Abstract  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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