Speaker: Ryan Kinser, University of Iowa

Title: New inequalities for subspace arrangements

Abstract: For each positive integer n > 3, we give an inequality satisfied by all rank functions of arrangements of n subspaces. When n=4, it is Ingleton's inequality, and for higher n these are all new inequalities (unable to be trivially obtained from inequalities involving fewer subspaces). These inequalities can be thought of as a hierarchy of necessary conditions for a (poly)matroid to be realizable. Some open questions about the "cone of realizable polymatroids" will be presented. Time permitting, motivation from the field of Information Theory will be discussed. Reference: arXiv:0905.1519