Title : Linear and monomial polyhedra : Geometry and applications

Abstract : We investigate size properties of a class of non-Euclidean
balls defined by a large number of polynomial inequalities. In the real
setting, this leads to $L^p$ bounds for the associated maximal operator.
In the complex version of the problem, we use these balls to obtain sharp
estimates for the Bergman kernel (on the diagonal) of a family of weakly
pseudoconvex domains in $\mathbb C^n$. This is joint work with Alexander
Nagel.