B-Calculus Mini Seminar

Here are the written notes in Romanian (but we always discuss much more than what is written in my prepared notes, thanks to the super-active audience!)

Written notes

Seminars 1&2 (Weak manifolds with corners, manifolds with corners, codimension of a point, b-maps, boundary-defining functions, b-vector fields, blow-up of a point).

Seminars 3&4&5&6 (Recall, Blow-up of a point, blow-up of a p-submanifold, comutting blow-ups, b-tangent bundle, b-normal bundle).

Seminars 7&8 (Lifting b-vector fields, index sets, polyhomogeneous conormal functions on R_+ and R^2_2).

Seminars 9&10 (Motivation: why are we interested in asymptotics with log terms, polyhomogeneous conormal functions on manifolds with corners, Pipeau about b-pseudodifferential operators).

Seminar 11 (denisities, b-densities, push-forward of densities, The Push-Forward Theorem (statement)).

Seminars 12&13&14 (Example for PFT, b-fibrations in coordinates, Distributions).

Seminars 15&16 (Hormander symbols, Classical symbols, radial compactification of R^n, conormal distributions on R^n; held by Rares Stan).

Seminar 17 (Conormal distributions to the zero section of a vector bundle, conormal distributions I^m(X,Y), pseudodifferential operators on compact manifolds (two definitions).

Seminars 18&19 (Wavefront set of a distribution, multiplication of distributions).     

Seminar 20 (Pseudo-differential operators on R^n).                           

We took a holiday break and we plan to finish the b-Calculus Seminar in September.

(Some) References:

-Singular Analysis Course lecture notes (Daniel Grieser).

-The Green book Atiyah-Patodi-Singer index theorem (Richard. B. Melrose).

-Singular Asymptotic Lemma and the Push-forward theorem (pdf) (Daniel Grieser, Michael. J. Gruber).

-Calculus of conormal distributions on manifolds with corners (Richard Melrose).

-A spinorial approach to Riemannian and Conformal Geometry (Jean-Pierre Bourguignon, Oussama Hijazi, Jean-Louis Milhorat, Andrei Moroianu, Sergiu Moroianu).

-Regularity for eigenfunctions of Schrödinger operators (pdf) (Bernd Ammann, Catarina Carvalho, Victor Nistor).

-Basics of the b-Calculus (pdf) (Daniel Grieser).