Wilfrid Gangbo

**Mass transport problems, its Connections and Applications**

**ABSTRACT**. These lectures are introduction to the
Monge-Kantorovich Theory (MKT). The basic problem, which occurs
naturally in economics, can be formulated as: Given two probability
measures on , representing the distribution of production
and consumption for some commodity, the problem is to
determine the most efficient way to rearrange the mass of the first
distribution to yield the second. Efficiency is measured against a
function which specifies the cost per unit mass for
transporting mass from
to
. We
develope the basic theory of optimal maps and state fundamental
results recently obtained by various authors. Applications we plan
to cover are dynamical evolution problems which appear in fluids
mechanic and kinetic theory. As time permits, we will mention
applications to shape optimization.