Colloquium: Floer-Fukaya-Gromov theory and field theory

by Yakov Savelyev (CRM-Montreal)

2013.03.11 | Jane Jamshidi

Date Thu 14 Mar
Time 14:00 15:00
Location Aud. D2 (1531-119)


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.

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