Mikolaj Fraczyk: "Mod-2 homology growth in higher rank lattices"

mardi 8 déc. 2020, 16:00 → 17:00 Europe/Paris

Abstract: It is known since late 70’s that in locally symmetric spaces of large injectivity radius, the k-th real Betti number divided by the volume is approximately equal to the k-th L2-Betti number. Is there an analogue of this fact for mod-p Betti numbers? This question is still very far from being solved, except for certain special families of locally symmetric spaces. In this talk I want to advertise a relatively new approach to study the growth of mod-p Betti numbers based on a quantitative description of minimal area representatives of mod-p homology classes. In case p=2 it yields very general results on the growth of first homology groups of lattices in higher rank Lie groups.