Abstract:
Homological methods in commutative algebra and representation theory can be traced back to the end of nineteenth century, around the time Hilbert proved his celebrated Syzygy Theorem. In this talk, I will introduce one of the most fundamental tools in homological algebra: the Ext functor.
My goal is to motivate its construction, state some famous conjectures (e.g. the Auslander-Reiten Conjecture) and show you glimpses of current research. For most of the talk, I will only assume elementary linear algebra knowledge.