Boij Soderberg theory of Betti tables of graded modules

In this talk I will describe the Boij-Soderberg theory of Betti tables of graded modules. The Betti table describes numerical data related to a minimal free resolutions of a graded module. The basic idea goes back to Hilbert who first proved existence of finite free resolutions. Recently Boij and Soderberg made striking conjectures about the general shapes of Betti tables. It allows to say (up to an integer multiple) which Betti tables actually exist. These conjectures were subsequently proved by Eisenbud and Schreyer.

I will define all the basic notions concerning resolutions and Betti tables, no knowledge of these questions will be assumed.