QM Research Seminar: Finite dimensional differential graded algebras

Speaker: Greg Stevenson (AU)

Abstract:

Differential graded algebras, which consist of a graded algebra together with a square-zero derivation, are an algebraic way of modelling multiplication up to homotopy. They are well adapted to, and arise naturally from, the study of derived categories in algebraic geometry. In general, the presence of the derivation makes these very complicated objects which are not necessarily amenable to usual techniques from ring theory.

In my talk I'll explain some recent results, by my student Isambard Goodbody and others, in the setting where the underlying algebra is finite dimensional over some field. In this case, a surprising number of results from the theory of finite dimensional algebras can be generalized to the differential graded setting.