Dynamical upper bounds for homological gradient invariants

We provide upper bounds for logarithmic torsion homology growth and Betti number gradients over fields along chains
of finite index normal subgroups. These upper bounds are phrased in the language of ergodic theory of groups and
quantitative homological algebra. In this talk, I will outline this framework and illustrate it in simple examples.

Based on joint work with Kevin Li, Marco Moraschini, Roman Sauer, and Matthias Uschold.