Séminaire de Mathématique

Effective Geometric Unlikely Intersections and Applications 1/2

by David Urbanik (IHES)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

Séminaire informel sur les intersections atypiques

This is part one of a two part lecture, the second of which will be given by Greg Baldi. In the first part we introduce a unified framework for studying "geometric" unlikely intersection problems, which in particular includes all such problems arising from (mixed) Hodge theory, and prove a general geometric Zilber-Pink theorem in this context, subsuming previous results of this nature. The proofs are also effective, in the sense that they give explicit algorithms to compute the relevant atypical loci. In the second part we will explain how this common framework also applies to characterise geometric unlikely intersection phenomena beyond the Hodge-theoretic setting, and in particular to orbit closures in strata of abelian differentials.



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Organized by

Emmanuel Ullmo