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Floer-Fukaya-Gromov theory and field theory

Yakov Savelyev
(CRM-Montreal)
Colloquium
Thursday, 14 March, 2013, at 14:00-15:00, in Aud. D2 (1531-119)
Abstract:
We first review some constructions in Gromov-Witten and Floer theory, particularly quantum homology and then discuss some related field theoretic constructions in the geometric context of a Hamiltonian fiber bundle over a smooth manifold, which could be thought of as one mathematical model for space time.
In particular we will explain construction and significance of quantum characteristic classes, their connections to Bott periodicity and classical Chern classes, and some other applications. If time permits we also indicate a construction of a new object associated to data above, which recovers the old theory but at the same time has a true local to global principle, which should theoretically make it more amenable to computation. This object comes from a kind of globalization of Fukaya category, from fibers of a Hamiltonian fibration over a smooth manifold, to the total space.
Organised by: QGM
Contact person: Jørgen Ellegaard Andersen