Special Lecture Professor Eckhard Meinrenken- March 17, FME, room 101 at 16h

Title: Normal form results in differential geometry

Abstract: A vector field on R^n is "Euler-like" if it is equal to the Euler vector field, up to higher order terms. Euler-like vector fields

can always be linearized, by an essentially unique change of coordinates. This basic fact gives rise to quick proofs of various

normal form results in geometry, such as the Morse lemma and the Darboux theorem. We shall also discuss linearizability of Euler-like vector fields along submanifolds N of a manifolds M, and some of its consequences. This will involve tubular neighborhood embeddings of normal bundles, and deformation spaces.