GAMP seminar by Kenro Furutani (Tokyo University of Science)

GAMP (Geometric Analysis and Mathematical Physics) Seminar.

Speaker: Kenro Furutani (Tokyo University of Science)

Title: Eigenvalue theorem for sub-Laplacian and Lagrangian submanifolds satisfying Maslov quantization condition

Abstract: Starting from N. Bohr model, Eigenvalue Theorem by A. Weinstein is a historical consequence guaranteeing the existence of quantum states based on a classical mechanical data, that is the existence of a Lagrangian submanifold in the phase space satisfying Maslov quantization condition implies a series of eigenvalues of the Laplacian. A rigorous proof is given based on the Fourier integral operator theory.

In this talk, I will remark that the result can be generalized to "sub-Laplacian" case and discuss the behavior of Lagrangian submanifolds under Riemann submersion.

Finally I will give an example of a Lagrangian submanifold satisfying Maslov
quantization condition by emphasizing the Maslov index defined for paths.