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.
