Geometric Analysis and Topology Seminar

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Symplectic Categories

Speaker: Alan Weinstein, UC Berkeley

Location: Warren Weaver Hall 512

Date: Wednesday, April 7, 2010, 3:45 p.m.

Synopsis:

Quantization problems suggest that the category of symplectic manifolds and symplectomorphisms should be augmented by the inclusion of more general morphisms, namely canonical relations, i.e. lagrangian submanifolds of products. It is well known that these relations compose well when a transversality condition is satisfied, but the failure of this condition to hold in general means that they do not comprise the morphisms of a category.

In this lecture, I will discuss several existing and potential remedies to the transversality problem, with an emphasis on those which involve allowing lagrangian "objects" more general than submanifolds.