The real orbits of complex Lagrangian Grassmannians

Abstract: The Riemann sphere can be broken up into three orbits of SL(2, R), as two open hemispheres and a great circle. We will discuss a generalization of this phenomenon in complex Lagrangian Grassmannians of higher dimensions under the action of the real symplectic group. We will give formulas for the number of orbits, incidence relations, and their dimensions. We will also show homotopy equivalences between these orbits and some other Grassmannian objects, and if time permits, a strategy to compute their homology.

differential geometrydynamical systemsgeometric topologysymplectic geometryspectral theory

Audience: researchers in the topic

Geometry and Dynamics seminar

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