Srikanth Iyengar: Extremal modules over commutative local rings

Over a commutative local ring R, it is known that the rate of growth of the Betti numbers of finitely generated modules is bounded above by that of the residue field of R. “Extremal modules” are those that achieve this upper bound. In my talk I will discuss some new results which demonstrate the ubiquity of extremal modules. It will be based on recent work with Luchezar Avramov and Claudia Miller, reported in our preprint: Homology over local homomorphisms, available on the arXiv.