Monday

We will begin by discussing rather broadly the relationship between nilpotent groups and curvature. There turn out to be surprising and deep connections, beginning in some sense with the work of Gromov on almost flat manifolds and the polynomial growth groups, but also with the works of Milnor on the fundamental groups of Ricci curvature. These works were extended by Fukaya/Yamaguchi and later Kapovitch/Wilking in order to understand more completely the fundamental groups of spaces with lower sectional and lower Ricci curvature bounds. The first part of this talk will give a broad introduction to these ideas and concepts, hopefully with relatively minimal background requirements, and hopefully with a focus on the leftover open questions and conjectures from the topic. The last part of the talk will focus on some recent work with Brue and Semola, where we answer some of these questions. In particular, we show the existence of compact manifolds with nonnegative Ricci curvature which are not (uniformly) almost abelian.