** 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