A UK Research Network

Geometric mechanics arises mainly from the observation that most of the natural laws are governed by symmetry principles. This applies to both Hamiltonian/Lagrangian systems and certain types of dissipative systems. Over the years, all these systems were shown to allow for a unifying framework within the context of geometric mechanics. This, in turn, led to the development of a number of different directions, including geometric control theory, geometric fluid dynamics, variational integrators, and so on.

In recent years, yet another promising direction has emerged, known as geometric quantum mechanics. So far, the use of reduction by symmetry within quantum dynamics has only begun and has already opened up new perspectives in quantum control. This research network also pursues two other modern applications of geometric mechanics and symmetry: shape analysis and fluid models. While the first is motivated by its impact in image processing and diagnostic techniques, the focus on fluid models finds its justification in the high importance that continuum fluid models possess within many areas of physics and technology.

The apparently diverse topics in this endeavour all share deep concepts in geometry and symmetry that serve to unify the derivations of their fundamental equations and the interpretations of their solutions. For example, hydrodynamic models and methods of data assimilation for weather prediction are also used in fundamental applications of shape analysis for the comparison of biomedical images. Likewise, the study of geodesic flows in geometric mechanics is of central importance also in the analysis of the Fubini-Study geodesics in quantum dynamics and computation.

The AGM Network brings together three leading groups in applied geometric mechanics in the UK, respectively at Brunel University, Imperial College and the University of Surrey (where the AGM network is coordinated). It is hoped that joining these task forces will impact the future of geometric mechanics in the UK and abroad.

First Meeting: Geometric Fluid Dynamics -- University of Surrey, 16 June 2017

Second Meeting: Geometric Quantum Dynamics -- Imperial College, 7 December 2017

Third Meeting: Symmetry and Shape Analysis -- Imperial College, 15 June 2018