Manifolds with Special Holonomy and their Calibrated Submanifolds and Connections (12w5024)


(Abdus Salam International Center for Theoretical Physics, King's College London)

Robert Bryant (Duke University)

(University of Waterloo)

Conan Leung (Chinese University of Hong Kong)


The Banff International Research Station will host the "Manifolds with Special Holonomy and their Calibrated Submanifolds and Connections" workshop from April 29th to May 4th, 2012.

At the dawn of modern science, there was no distinction between physics and mathematics, particularly with geometry, the oldest "natural science". Famous scientists such as Newton, Lagrange, and Hamilton consistently studied mathematical questions inspired and motivated by physical considerations. Later, as research in both disciplines became much more specialized, the two sciences drifted apart. However, since the 1950's, we have witnessed a reconciliation, that has resulted in spectacular success both in physics and in mathematics, most notably in the areas of geometry and topology. The remarriage of physics and geometry began with the work of the physicists Yang and Mills, which attracted the attention of exceptional mathematicians such as Atiyah, Bott, and Singer. Many fantastic results were obtained in the next three decades, relating theories from physics with geometric and topological information about spaces.

The tradition of geometry and physics motivating and inspiring each other has continued since then. Much more recently, in the early 1990's, the unexpected and mysterious phenomenon of mirror symmetry of certain higher dimensional spaces was predicted by string theorists. The idea of mirror symmetry is that, although two spaces could appear to be very different geometrically, because they lead to equivalent theories of physics, there must be some deep, hidden link between these two spaces. This has now been, in many cases, verified rigorously by mathematicians, and has led to new applications to the solution of enumerative problems that were previously intractable. However, there are far more unanswered mathematical questions that can now be asked, that arise from such physical considerations. It is likely that their solution will again lead to unexpected applications. The workshop on "Manifolds with Special Holonmy and their Calibrated Submanifolds and Connections", to be held at the Banff International Research Station, will enable researchers in geometry and physics from around the world to assemble, exchange ideas, and make progress on these new and difficult questions.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).