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Grigory Mikhalkin


Speaker: Grigory Mikhalkin
Title: (p,q)-Homology Classes in Tropical Geometry
Affiliation: Universite de Geneve
Date: Friday, January 15, 2010
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. Just like their classical (complex) counterparts, tropical manifolds carry homology theories. In the talk we will look at the simplicial and singular homology groups of tropical manifolds. However, unlike the classical case, we can directly trace (p,q)-contributions (to the h^{p,q} Hodge numbers) already in this very topological language.

Furthermore, in good cases a tropical manifold is approximable by a 1-parametric family of complex manifolds. The tropical homology carries not only the corresponding degenerations of the Dolbeaut (p,q)-groups, but also the corresponding monodromy operator. Its tropical manifistation, the Picard-Fuchs "tropical wave" looks in many ways similar to the tropical hyperplane section.

The talk is based on a work in progress joint with I. Itenberg and I. Zharkov.