Colloquium: Kobi Peterzil (U. Haifa)

Thu, 21/10/202114:30-15:30
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Title: Algebraicity, analyticity and definability: from Zilber's conjecture to o-minimal GAGA

Abstract: Chow’s theorem says that a complex analytic projective variety is algebraic. A generalization of this result (proved with Starchenko 2009) says that the result holds also for affine analytic varieties, if in addition we assume that the variety is definable in an o-minimal structure. Since its proof the result has been applied to show algebraicity of sets in various settings, from Diophantine geometry to Hodge theory. 

In this survey talk I will describe a development of ideas, starting from general conjectures in model theory by Boris Zilber about the algebraicity of certain strongly minimal structures (1980’s), their subsequent refutation by Hrushovski (1990’s), the recovery of restricted versions of the conjecture by the additional assumption of o-minimality, leading up to the most recent o-minimal GAGA (by Bakker Brunebarbe and Tsimerman, 2018) and applications to Hodge theory. If time permits I will also mention slightly less known variations of the o-minimal Chow theorem.