Seminar talk, 19 October 2016
Speaker: Dmitri Alekseevsky
Title: Second order partial differential equations with a simple symmetry group
Let be the homogeneous space of a simple Lie group with an invariant contact distribution, which locally defined by a contact form . The non-degenerate 2-form is defined up to a conformal multiplier. The manifold of Lagrangian planes in is the total space of the bundle . The fiber is the Grassmannian of the Lagrangian planes of symplectic vector space . The group acts on as the automorphisms group, and the -invariant hypersurfaces are 2nd order equations with the symmetry group .
The talk will discuss the description of such hypersurfaces in the case when is the adjoint manifold of a simple complex Lie group , i.e., the orbit of a highest vector of Lie algebra in the projective space .
The talk is based on the joint work with Jan Gutt, Gianni Manno, and Giovanni Moreno.