Lagrangian manifolds and Hamiltonian systems, corresponding to asymptotic solutions of PDE's with singularities

• 主讲人：Andrey Shafarevich
• 举办方： Beijing-Novosibirsk Seminar on Geometry and Mathematical Physics
• 时间： 2022-04-28 15:00 - 2022-04-28 16:00
• 地点： online

 

Video: https://disk.pku.edu.cn:443/link/79E436355FC4F8183D5BB31C132F51C0
Valid Until: 2026-05-31 23:59

 

Abstract: Certain class of asymptotic solutions to PDE's with smooth coefficients is deeply connected with geometric objects - Lagrangian surfaces or complex vector bundles over isotropic manifolds. We study modifications of these objects for the case of PDE's with singularities which appear either in coefficients or on manifolds of independent variables.

 

Bio: Professor A.I.Shafarevich is currently the Dean of the Faculty of Mechanics and Mathematics at Lomonosov Moscow State University. He is also the Corresponding Member of the Russian Academy of Sciences.

The main scientific interests of A.I.Shafarevich lie in the field of mathematical physics, asymptotic and geometric theory of linear and nonlinear partial differential equations, quantum mechanics and hydrodynamics. He solved the problem posed by V.P. Maslov and widely discussed in the scientific literature on the multiphase asymptotics for the equations of hydrodynamics.