Michael Perlman (Minnesota)Title: Local cohomology, D-modules, and Schubert varietiesAbstract: A general problem in commutative algebra and algebraic geometry is to calculate the local cohomology modules associated to a subvariety of a smooth variety. In recent past, a great deal of progress has been made by taking advantage of a deeper structure, namely that of (mixed Hodge) D-modules. Another context in which D-modules appear is in geometric representation theory, for instance in the study of composition factor multiplicities of Verma modules over simple Lie algebras, which is the subject of the Kazhdan–Lusztig theorem. We will discuss how one may combine commutative algebra and Kazhdan–Lusztig theory to calculate local cohomology with support in Schubert varieties in generalized flag varieties. Our main example will be the case of the classical Grassmannian. Time permitting, we will mention applications to determinantal varieties and to other Lie types.
