Analysis Seminar: Chamsol Park (UNM), Mixed Hessian and folding singularities and their applications
Friday, April 26, 2019 -
2:00pm to 3:00pm
Title: Mixed Hessian and folding singularities and their applications
Abstract: When studying oscillatory integral operators, it is good to consider the canonical relation of the phase function. In this talk, we are going to look at the case where the projections of the canonical relation are local diffeomorphisms or not. When the projections are local diffeomorphisms, then the "mixed Hessian" of the phase function is nonsingular, which can be called "Hormander's condition." We also look at the case of having folding singularities. In this case, the projections are no longer local diffeomorphisms. After seeing them, we briefly review how to use these to find L^p norms of eigenfunctions of the Laplacian restricted to the geodesics of compact Riemannian manifolds without boundary, and explain why it is hard to find the estimates of the eigenfunctions restricted to higher dimensional submanifolds cases.
Contact Name: Maxim Zinchenko