Boris Shapiro: Deterministic and random crossing points in mathematical physics

Abstract:

Pencils of linear operators are indispensable in perturbation theory and mathematical physics in general. Crossing points are the value of the perturbation parameter for which the corresponding linear operator has a non-simple spectrum. In my talk I give some physically motivated examples of both deterministic and random pencils of operators as well as some information about the location and distribution of their crossing points.