The aim of this school is to present the basic tools from manifold theory and algebraic topology that allow one to study automorphism groups of manifolds. In the 70's a general theory of automorphism groups of manifolds was developed but it involves relatively "heavy machinery" such as smoothing and surgery theory. We aim to present a path into the field that keeps the machinery relatively light-weight. This involves studying diffeomorphisms by how they act on submanifolds, i.e. we will study spaces of embeddings or "knot theory in the large."

The school will begin with an introduction to manifold theory and algebraic topology, building towards the main tools in the field, such as the theory of fibre bundles, transversality and Embedding Calculus.

Lectures will be given by Gregory Arone (University of Stockholm, Sweden), Ryan Budney (University of Victoria, Canada), Stefan Friedl (University of Regensburg, Germany), Stephan Klaus (Oberwolfach Research Institute for Mathematics, Germany), Sergiy Maksymenko (Institute of Mathematics of NAS of Ukraine, Kyiv), Michael Weiss (University of Münster, Germany).

The school is intended for graduate and advanced undergraduate students who want to know the basics of manifold theory, in particular embeddings and automorphisms of manifolds.

Necessary prerequisites: knowledge of general topology (topological spaces) and abstract algebra (groups, rings, and modules).