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20th November 2000 to 21st November 2000

Original URL:

Isaac Newton Institute for Mathematical Sciences

Geometry and Topology of Fluid Flows

4 September to 17 December 2000

Organisers: H Aref (Urbana-Champaign), T Kambe (Tokyo), RB Pelz (Rutgers), RL Ricca (UCL)

Isaac Newton Institute for Mathematical Sciences, Cambridge, UK

Differential Geometry and Global Analysis in Fluid Dynamics and Dynamical Systems


20 - 21 November 2000

Organiser: Professor Tsutomu Kambe (Tokyo)

Programme (Tentative)

Speakers: K Bajer (Warsaw); P Boyland (Florida); D Ebin (SUNY); Y Fukumoto (Kyushu); D Holm (Los Alamos); T Kambe (Tokyo); B Khesin (Toronto); J Marsden (Caltech); P Michor (Wien); G Misiolek (Notre Dame); M Pettini (Firenze); R Ricca (UCL); E Spiegel (Columbia); V Zeitlin (LMD, Paris 6).

Programme Theme:Dynamical systems with finite or infinite number of degrees of freedom, such as hydrodynamics, magnetohydrodynamics, and various interable systems, often have certain symmetry groups. Recent advances in the description of behaviour of those systems are related to the study of differential geometry of the corresponding groups. The geometric theory allows one to describe both quantitative and qualitative global properties of trajectories of such systems.

For instance, the time evolution of a flow of an ideal incompressible fluid is governed by the geodesic equation on the group of volume-preserving diffeomorphisms. Kinetic energy defines the corresponding right-invariant metric on that group. Thus group theory and differential geometry provide a natural framework for the description of fluid motions. This approach, originally suggested by V.Arnold in 1966 for an ideal fluid, its later extensions to various media, magnetohydrodynamics, and integrable systems, as well as recent spectacular achievements in these areas, will be the subject of this workshop.

This scope of mathematical ideas gives a profound insight on the nature of various physical systems, both finite and infinite-dimensional, and opens new areas of their studies. Moreover, numerous applications to incompressible and compressible, homogeneous and stratified fluids, MHD fluid, rigid bodies, and many other dynamical systems proved to be fruitful for mathematical theories involved.

This meeting is being supported by Hewlett-Packard's Basic Research Institute in the Mathematical Sciences (BRIMS) and the Isaac Newton Institute.

Further Information: Lunch will be available for a nominal charge; please let Tracey Andrew at the Institute know by 31 October 2000 if you intend to come, to help us plan for lunch: telephone: (01223) 335984; fax: (01223) 330508. There are limited funds available to assist research students to attend: please apply by 31 October 2000 to Tracey Andrew at the Institute.

Scientific enquiries may be addressed to Professor Tsutomu Kambe.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons