Minimal models for monomial algebras

Mathematical objects of all types and flavors admit a notion of a 'model'. These are objects of the same type as our starting object of interest, which are better behaved, and are useful to obtain qualitative and quantitative information about it. Minimal models are "optimally small'' models that usually lend themselves to computation. Determining the minimal model of an object, when it exists, is generically a difficult task.

In this talk, I will explain how to obtain the minimal model of an associative algebra defined by monomial relations, as in 1804.01435. I will survey related results, and will mention some open questions and conjectures that emerged from 1804.01435 and related work 1909.00487 with Dotsenko and Gelinas.