Quasi-Projective Dimension (Luke Kershaw 12/03/21)

Microsoft Teams

This week we welcome Luke Kershaw from the University of Bristol to talk about Quasi-Projective Dimension. We will as usual be on Teams at 4pm on the Friday.

Abstract: “Projective dimension is an important invariant of modules that tells us how far a module is from being projective. We can use the projective dimension to measure how complicated the representation theory of a ring is. For example, in Mod-ℤ = Ab, the category of abelian groups, all modules have projective dimension at most one, illustrating the relative simplicity of the structure of abelian groups. However, some rings have modules of infinite projective dimension but still have pretty simple representation theory. Quasi-projective dimension is a generalisation of projective dimension that allows us to measure some of that simplicity. This talk will begin with a review of projective dimension before introducing quasi-projective dimension and some of its properties.”