Jingyin Huang: Uniform lattices acting on RAAG complexes
A classical result by Bieberbach says uniform lattices acting on Euclidean spaces are virtually free abelian. On the other hand, uniform lattices acting on trees are virtually free. This motivates the study of commensurability classification of uniform lattices acting on RAAG complexes, which are cube complexes that "interpolate" between Euclidean spaces and trees. We show the tree times tree obstruction is the only obstruction for commmensurability of label-preserving lattices acting on RAAG complexes. Some connections of this problem with Haglund and Wise's work on special cube complexes will also be discussed.
