## Workshop on Optimal Transportation,
Transport Equations, and Hydrodynamics
### 11-15 July 2005, Edinburgh
**Home Page | Workshop Arrangements | Scientific Programme and Participants**
**Report on meeting now available from this link**
Organisers
Yann
Brenier (CNRS Nice/Paris VI)
Geoffrey
Burton (Bath)
Optimal
Transportation theory arose from Monge's mass
transfer problem of 1781. Since the
1980s, there has been an upsurge in activity stimulated by the
discovery of the
monotone rearrangement and polar factorisation of vector valued
functions. Through this result, optimal
transportation was
related to the Monge-Ampere equation, an important nonlinear PDE
arising in
differential geometry.
Ideas
from optimal transport theory are now finding
applications in such diverse fields as statistical mechanics,
convexity, and integral
and geometric inequalities.
Since
the first existence theorems for solutions of
the Euler equations with discontinuous vorticity were proved in the
1960s,
there have been further developments in the realm of weak solutions in
hydrodynamics. These developments fit well with the theory of transport
by
non-smooth vector fields which arose in the 1980s, establishing
properties characteristic
of the flow of vector field in a context where the trajectories of the
flow
were not always well-defined, and which are now
able to cope with divergence-free BV vector
fields.
One
of the most exciting models in fluid mechanics,
combining both optimal transportation and the theory of transport
equations, is
the semigeostrophic model of large-scale phenomena in vortex flows.
The
workshop seeks to bring together specialists in
the three topics of its title, to present the latest developments in
each, and
to investigate the connections between them.
Numbers
of participants are limited. Anyone interested
in attending should contact
Geoffrey
Burton (grb@maths.bath.ac.uk);
the
organisers
will issue an invitation if space permits.
*Created 12 April 2005*
This workshop is made possible by grants awarded to
ICMS from EPSRC
Mathematical Sciences Programme, the Scottish Higher Education Funding
Council and the London
Mathematical Society.
**Home Page | Workshop Arrangements | Scientific Programme and Participants** |