Title: Computing Free Resolutions of OI-Modules

Abstract: Free resolutions are a powerful tool in commutative and homological algebra. Much of the structure of a module can be encoded in a free resolution. For example, in the case of graded modules, free resolutions can be used to study Betti numbers and Hilbert functions. Certain homological constructions such as the Ext and Tor functors can be computed with free resolutions as well. In this talk we show how to compute free resolutions in the case of OI-modules over a Noetherian polynomial OI-algebra, where OI denotes the category whose objects are totally ordered finite sets and whose morphisms are strictly increasing functions.