Rough paths on manifolds 1 - Minicourse

04.10.2016, 10:00 Uhr  –  Haus 9, Raum 2.22
Arbeitsgruppenseminar Analysis

Youness Boutaib

 The general aim of this course is to present ways of translating

   notions from classical analysis (understood to be built for and

   adapted to the Euclidean setting) to manifolds without adding too

   much structure on the manifolds trying to mimic the same

   constructions. We use the theory of rough paths as an example to

   show these ideas (but also for its own merit as the predecessor

for the ideas behind the currently much celebrated regularity

   structures). During the first lecture, we will briefly review the

   main ideas behind the theory of (geometric) rough paths (as

   introduced by Terry Lyons) that will enable us to achieve our goal

   in the following two lectures. Time allowing, these ideas will

   include:

   * The p-variation as a way of measuring the smoothness/regularity

   of paths;

   * Stieltjes and Young's integration theories and their limits;

   * Signatures of moderately irregular paths;

   * Geometric rough paths and rough differential equations.