Each year the Sofia Kovalevskaya lecture takes place at the Faculty of Mathematics at Bielefeld University. It is in honour of the Russian female mathematician with that name, and is given by a successful or promising female mathematician, who is chosen by a jury.
Abstract: In this talk, we will discuss the class of CAT(0) groups. A finitely generated group G is a CAT(0) group if G acts properly discontinuously and cocompactly by isometries on a CAT(0) space. We will recall several well-known examples as well as non-examples in the hopes of understanding methods for constructing CAT(0) spaces as well as obstructions for showing that no such space can be found. We will also discuss groups for which the question of being CAT(0) is still open. It is a well-known open problem to decide whether the braid groups on more than 7 strands are not known to be CAT(0) or not. We will focus on a different family of examples - namely, the automorphism groups of right-angled Coxeter groups and their subgroups.