Homological ubiquity of quasi-poynomials in multigraded algebra

In commutative algebra, functors such as local cohomology, Ext, and Tor applied to sequences of modules often grow quasi-polynomially, i.e., they grow periodically along finitely many polynomials. In this work we use the theory of tame modules from persistent homology and Presburger arithmetic to provide an explanation for this quasi-polynomial behavior in the multigraded setting. This is joint work with Hailong Dao, Ezra Miller, Christopher O’Neill, and Kevin Woods.