Infinite dimensional Riemannian geometry and stochastic geometric mechanics

Welcome

Mathematical analysis in infinite dimensions deals, for example, with fluid flows, shape changes, and probability distributions. All of these fields benefits from methods of infinite dimensional geometry and symmetry. For example, the symmetry of Eulerian fluid dynamics under Lagrangian particle relabelling corresponds to right-invariance of kinetic energy metrics under smooth invertible maps (diffeomorphisms). This invariance enables the Lie-Noether symmetry methods of mechanical systems and geometric mechanics to be applied to Eulerian fluid dynamics, and also transfer to the other two related fields. Likewise, stochastic geometric methods for quantifying uncertainty in fluid flows transfer directly into methods for estimating errors in detecting shape changes which may be crucial, e.g, in medical images such as MRI.

The workshop will bring together experts from all three fields to explore the newly-recognised synergistic intersections among the rapidly evolving fields of infinite dimensional Riemannian geometry, stochastic geometric mechanics and their applications. The workshop aims to advance theoretical developments, exchange methods and solution techniques between the fields, and identify shared open problems and future research directions, from both theoretical and applied viewpoints.

Participation

The workshop is by invitation only. If you are interested, please contact one of the organizers.

Organization

The workshop is funded by ICMS and the London Mathematical Society.

Organizing committee:

• Martin Bauer (University of Vienna)
• Alice Le Brigant (University Paris 1)
• Darryl Holm (Imperial College)
• Stefan Sommer (University of Copenhagen)

Scientific Advisory Committee:

• Carola-Bibiane Schönlieb (University of Cambridge)
• Boris Khesin (University of Toronto)
• Tudor Ratiu (Shanghai Jiao Tong University)
• Peter W. Michor (University of Vienna)
• Marc Arnaudon (University of Bordeaux)