The Oberwolfach conference "Topologie" is one of only a few opportunities for
researchers from many different areas in algebraic and geometric topology to meet and
exchange ideas. On this occasion, because of the Corona pandemic, only about 20 participants attended in person, but another $\sim$ 25 attended online. Speakers were selected from both groups. A topic of special interest emphasized at the workshop was the rational
homotopy theory of embedding spaces and relations to graph complexes and formality. Two 50 minute lectures
on this theme were given by Thomas Willwacher, and one by Victor Turchin.
The rest of the program covered a wide range of topics, among them: homotopy properties of diffeomorphism groups
of high dimensional manifolds, advances in the classification of high-dimensional highly connected smooth manifolds,
parametrized algebraic surgery in relation to hermitian algebraic K-theory, other advances in
and geometric applications of algebraic K-theory, stable homotopy interpretation of link invariants,
geometry of surface bundles and cohomology of mapping class groups, boundary concepts in
geometric group theory, and Koszul duality for operads.