16 mai 2018

Farhad Babaee (Fribourg (Suisse))
Complex tropical currents, and approximability problems

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Lieu : IMO Salle 3L8

Résumé : Demailly (2012) showed that the Hodge conjecture is equivalent to the statement that any (p,p)-dimensional closed current with rational cohomology class can be approximated by linear combinations of integration currents ; Moreover, the statement that all positive currents with rational cohomology class can be approximated by positive linear combinations of integration currents implies the Hodge conjecture (1982). In this talk, I will explain how basic ideas from tropical and toric geometry can lead to construction of a family of currents which does not satisfy the latter statement in any dimension and codimension higher than 1. The talk is based on collaborations with June Huh and Karim Adiprasito.

Complex tropical currents, and approximability problems  Version PDF