Resolutions of letterplace and co-letterplace ideals

The study of resolutions and syzygies of modules has been a topic of interest for commutative algebraists and algebraic geometers since the work of David Hilbert and, more recently, the inception of homological algebra.

The aim of this talk is twofold. The first half will serve as a very brief introduction to the subject, with a focus on its combinatorial aspects. As an application, in the second half we will present some results on some ideals associated with posets (joint work with Gunnar Fløystad and Amin Nematbakhsh), giving a common framework for many well-studied classes of ideals. The techniques used to prove these results are both topological-combinatorial and algebraic.