Boij-S\"oderberg theory: Introduction and survey
  Boij-S\"oderberg theory describes the Betti diagrams of graded modules over the polynomial ring up to multiplication by a rational number. Analog Eisenbud-Schreyer theory also describes the cohomology tables of vector bundles on projective spaces up to rational multiple. We give an introduction and survey of these newly developed areas. 
Gunnar Floystad
math.AC