Seminar “Quasi-classical (short-wave) asymptotics and the canonical Maslov operator”
On
The laboratory “Nonlinear and nonlocal problems of mathematical Physics and their applications” of RUDN together with MIAN conducts a series of mini-courses on modern analysis on the topic: “Quasi-classical (short-wave) asymptotics and the canonical Maslov operator”.
Speaker: Nazaikinsky Vladimir, Corresponding Member of the Russian Academy of Sciences, A.Y. Ishlinsky Institute of Problems of Mechanics RAS.
The canonical operator is a tool that allows you to build global asymptotics in various problems of mathematical physics.
The existing statements of its design in most cases are very voluminous and full of technical details, which can create a barrier to entry into the subject.
The mini-course is an introduction to the theory and practice of using the canonical operator that is understandable for non-specialists.
The following issues will be raised:
- Problems with a small parameter and quasi-classical asymptotics.
- The main geometric objects (Lagrangian manifolds, Maslov index) on which the construction of the canonical operator is based.
- Canonical operator, as a “black box”: the minimum set of information necessary to solve the Cauchy problem and the eigenvalue problem using the canonical operator.
- The internal structure of the canonical operator.
- Computationally efficient implementations of the canonical operator, in particular, representation via special functions in the vicinity of caustics of general position.
- Canonical operator in problems with the right side, boundary value problems, lattice problems.