Grassmann Varieties, Codes and Combinatorics,   Sudhir R. Ghorpade,   Indian Institute of Technology,,  Fri, 29 June, 2012,   2:00 p.m. C-356


Given a finite dimensional vector space, the set of all its subspaces of a fixed dimension turns out to be the locus of zeros of a bunch of quadratic homogeneous polynomials. This is known as a Grassmann variety and it is a basic object in many branches of mathematics including algebraic geometry, topology and Lie theory. We will begin an elementary introduction to Grassmann varieties and then discuss several results and questions concerning classes of linear codes associated to Grassmann varieties and their Schubert subvarieties over finite fields. It will be seen that there are strong relations with many aspects of combinatorics, especially, enumerative combinatorics and also to graphs and matroids. An attempt will be made to keep the prerequisites at a minimum.