Pure Maths Colloquium: Exact Lagrangian immersions revisited
13 May 2013 16:00 in CM221
Symplectic manifolds contain a distinguished class of submanifolds, Lagrangian submanifolds, which are defined by a system of differential equations, and which play a role in dynamics, topology, quantum mechanics and elsewhere. Gromov proved that immersed Lagrangian submanifolds are much more common than embedded ones: the former tend to be flexible, the latter rigid, part of his famous "soft-hard" dichotomy in geometry. We revisit this subject and consider exact Lagrangian immersions in standard flat Euclidean space which have the simplest possible singularities, and find that the soft-hard borderline is more delicate than had been previously imagined. The talk reports on joint work with Tobias Ekholm.
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