Growth of mod-p homology in higher rank lattices

Abstract: It is known since the late 70s 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 $L^2$ 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.

group theorygeometric topologymetric geometry

Audience: researchers in the topic

McGill geometric group theory seminar