Will give a Topology Seminar entitled: Categorical dynamics on stable module categories
Abstract: Given a mathematical object X and an endomorphism f of X, entropy assigns to this pair a number h(f) measuring the dynamical complexity of f. Initially defined for measure spaces and topological spaces, it has also been generalized by Dimitrov–Haiden–Katzarkov–Kontsevich to measure the complexity of endomorphisms of stable ∞-categories. I will discuss a result showing that the categorical polynomial entropy of a twist functor on stable module categories of certain algebras A of cohomology operations over a field k reflects the complexity of A: it is at least one less than the Krull dimension of H*(A;k), generalizing results of Fan–Fu–Ouchi. We will then discuss work in progress to bring this dynamical perspective to homotopy theory.
