Video library: V. E. Nazaikinskii, Uniformization of degenerate equations and semiclassical asymptotics

VIDEO LIBRARY


International Conference Dedicated to the 100th Anniversary of the Birthday of V. S. Vladimirov (Vladimirov-100) January 12, 2023 13:30, Moscow, Steklov Mathematical Institute, room 430 (Gubkina 8) + Zoom

Uniformization of degenerate equations and semiclassical asymptotics V. E. Nazaikinskii Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
Abstract: For a stratified manifold $X$ that is the quotient of a smooth compact manifold $M$ by a compact Lie group action, we define smooth functions on $X$ as invariant smooth functions on $M$ and $h$-(pseudo)differential operators on $X$ as the restrictions of invariant $h$-(pseudo)differential operators on $M$ to the space of smooth functions on $X$. We discuss semiclassical asymptotics for pseudodifferential equations on $X$; examples include boundary degenerate linearized shallow water equations describing the run-up of long waves on a shallow beach and $h$-pseudodifferential equations on orbifolds. Language: English