Image: D.D. Holm, T. Schmah & C. Stoica. Geometric Mechanics and Symmetry:
From Finite to Infinite Dimensions, Oxford University Press (2009).
Geometric mechanics arises mainly from the observation that most of the natural laws are governed by symmetry principles. This applies to both Hamiltonian and Lagrangian systems, and certain types of dissipative systems, such as geophysical fluids with irreversible processes, the porous media equation or ferromagnetic dynamics. Over the years, all these systems were shown to allow for a unifying framework within the context of geometric mechanics. This in turn has led to the development of a number of different directions, including geometric fluid and plasma dynamics, geometric control theory, geometric and mimetic numerical schemes, and so on.
The London Mathematical Society has funded the Applied Geometric Mechanics Network. It links Edinburgh, Exeter, Imperial, and Surrey. The node leaders are Prof Darryl Holm (Imperial), Dr Cesare Tronci (Surrey), Prof Jacques Vanneste (Edinburgh), and Dr Hamid Alemi Ardakani (Exeter).
The AGM Network aims to continue the joint research programme in Applied Geometric Mechanics, originally initiated by the Department of Mathematics at the University of Surrey in 2014 (link here), which has been so fruitful and stimulating in previous years. In the past, the AGM programme has sought to bring together the leading research groups in geometric mechanics and symmetry based at Imperial College London, University of Surrey, Brunel, and City, University of London.
The new series of AGM Meetings aims to bridge the gap between the two leading groups in applied geometric mechanics in the Southeast UK (Imperial: Prof Darryl Holm and collaborators; University of Surrey: Nonlinear Waves and Geometric Fluid Dynamics Group), and the Centre for Geophysical and Astrophysical Fluid Dynamics (GAFD) at the University of Exeter, in the Southwest UK, and the Applied and Computational Mathematics Group (ACM) at the University of Edinburgh, in Scotland, who are also interested in applications of geometry and symmetry to physical systems. The GAFD Research Group is particularly active in applications of differential geometry, topology, and geometric mechanics in the development of continuum theories, conservation laws, and discrete geometric methods for geophysical fluid dynamics, and magnetohydrodynamics (MHD) problems, and in the development of geometric and structure-preserving numerical methods for weather and climate dynamics. The group especially benefits from close collaborations with the Met Office as well as numerous ties to the astrophysical community. The ACM Group at Edinburgh has expertise in applications of geometric methods to oceanography, specifically the development of parameterisations of meso- and sub-mesoscale eddies and the interactions between both surface and internal gravity waves with currents. We are excited about the new perspectives the GAFD Group at Exeter and the ACM Group at Edinburgh will bring to the programme. It is hoped that joining these task forces will impact the future of geometric mechanics in the UK and abroad.