Title: Combinatorial recipes for rings in mixed characteristic

Abstract: There are many theorems for equicharacteristic rings which are still open in the mixed characteristic setting. This creates a demand for concrete examples of rings with a uniquely mixed characteristic flavor. I present a general recipe for interesting mixed characteristic rings; the idea is to expand the definitions of classical combinatorial rings, such as Stanley-Reisner rings or toric rings, by replacing monomials with "p-monomials". I will present the properties of these p-monomials in general and discuss several classes of p-monomial based rings.