Seminar

I will first describe a general construction of semi-classical functions  associated to isotropic submanifolds, both in cotangent and symplectic contexts. Such functions  have symbols that are symplectic spinors, and I will sketch their symbol calculus. This is the semi-classical analogue of the Boutet de Monvel-Guillemin theory of Hermite distributions. The main, new applications I will discuss are to the so-called Hermite operators, whose kernels are isotropic distributions associated to submanifolds of the diagonal. Examples include certain mixed states, for which we obtain a Szegö limit theorem.