Caroline Klivans (Brown)

Projection volumes of hyperplane arrangements

Motivated by the problem of calculating p-values for linear restricted
statistical hypothesis testing, we considered projection volumes of
polyhedral cones.  Our main result shows that projection volumes are
given by the coefficients of the characteristic polynomial of an
associated arrangement.  In the case of Coxeter arrangements, these
results naturally extend those of De Concini and Procesi, Stembridge,
and Denham which establish the relationship for 0-dimensional
projections.  The methods used here will be combinatorial.  I will not
assume familiarity with any of the above topics for the talk.