Turbulent convection and dynamo
activity are the most challenging unresolved problems in
the physics of rotating late--type stars like the Sun,
where they play a fundamental role in such processes as
the transport of energy, mixing of specific angular
momentum, generation of magnetic fields, and basic
stellar variability. We propose to combine advanced
scientific, mathematical and computational analyses with
state-of-the-art computational technology to attack these
problems by means of very high resolution hydrodynamical
and magnetohydrodynamical numerical simulations. Such
simulations will serve the unique purpose of fostering
technological advancement in high performance computer
architectures as means to solve fundamental scientific
issues.