Local cohomology was introduced by Grothendieck in 1961. Since its introduction, the theory has been developed in a number of different directions and draws connections with topology, geometry, and combinatorics. Algebraically, local cohomology modules can be used to measure the dimension and depth of a module over an ideal. As a consequence, local cohomology can be used to test if a ring is Cohen-Macaulay or Gorenstein. Additionally, local cohomology can be used to partially answer the question of how many generators an ideal has up to radical.

This talk will be a brief introduction to local cohomology. As an application, we will discuss a proof of the prime characteristic case, without using Tight Closure Theory, of Hochster and Roberts Theorem on the Cohen-Macaulayness of direct summands of regular rings. Speaker(s): Andrés Servellón (University of Michigan Ann Arbor)