The University of Michigan Combinatorics Seminar
Let G be a compact group acting in a real vector space
V. I will describe a family of inequalities relating the
L-infinity norm of a matrix element of the representation
of G with its
Lp norm for p less than infinity.
The results are applied to obtain
approximation algorithms to find the maximum absolute value
of a given multivariate polynomial over the unit sphere (in which
case G is the orthogonal group) and for the multidimensional
assignment problem, a hard problem of combinatorial optimization
(in which case G is the symmetric group).