Andrew Wiles Building
Radcliffe Observatory Quarter
Oxford OX2 6GG, UK
Organisers: Jock McOrist (Surrey), Ian Roulstone (Surrey), Martin Wolf (Surrey)
Photograph by Sean O'Flaherty
The application of ideas from the theory of complex manifolds to fluids mechanics has revealed important connections betwen complex structures and the dynamics of vortices in many different fluid flows. Large-scale atmospheric flows, optimal transport and complex geometry have each provided a framework for studying (Monge-Ampère) partial differential equations, their transformation properties, and solutions. Recently, new connections have been established between these seemingly disparate areas, as well as between coherent vortices in incompressible Navier-Stokes flows and almost-complex structures. The application of geometry to fluid mechanics has opened up promising new perspectives on some enduring problems, and facilitates a unification of otherwise ostensibly disparate topics, including singular behaviour, conservation laws, and the PDEs describing vortex dynamics.
The interplay between hyper-Kähler geometry and the Monge-Ampère equation also has a long cherished history in string theory, a subject far-removed from fluid dynamics. Recently, several new tools have been developed, such as generalized geometry, flux compactifications, and string theory dualities for understanding the structure of these equations and their solutions.
The aim of this workshop is to bring together experts from complex manifolds and string theory with those from fluid mechanics to study the interplay between geometry, optimal transport, and applications.
The workshop will focus on the following topics
Participation in the workshop is by invitation. Some additional places may be available, please email Naomi Kraker to register your interest.