The space of positive Lagrangian submanifolds
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Tue, 05/02 15:45 |
Jake Solomon (Jerusalem) |
Algebraic and Symplectic Geometry Seminar  |
L3 |
| A Lagrangian submanifold of a Calabi-Yau manifold is called positive if the real part of the holomorphic volume form restricted to it is positive. A Hamiltonian isotopy class of positive Lagrangian submanifolds admits a Riemannian metric with non-positive curvature. Its universal cover admits a functional, with critical points special Lagrangians, that is strictly convex with respect to the metric. If time permits, I'll explain how mirror symmetry relates the metric and functional to the infinite dimensional symplectic reduction picture of Atiyah, Bott, and Donaldson in the context of the Kobayashi-Hitchin correspondence. | |||