The Simons Foundation is pleased to announce the establishment of the Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics, directed by Robert Bryant at Duke University. The collaboration will advance the theory and applications of spaces with special holonomy and the geometric structures and calibrated submanifolds and instantons associated with them, particularly in two exceptional cases: spaces with holonomy G2 or Spin(7) in seven or eight dimensions, respectively.
The best-understood special holonomy spaces are the so-called Calabi–Yau spaces; over the past 30 years, the study of these from various viewpoints and geometry, analysis, algebra and physics has been one of the most active and influential parts of mathematics and its applications to physics. Meanwhile, the exceptional cases, which share some important features with Calabi–Yau spaces, remain the most challenging and the least understood, both mathematically and physically. Exceptional holonomy spaces are key ingredients in extracting physics from M-theory and F-theory (generalizing the role that Calabi–Yau 3-folds play in string theory), where they provide models for the extra dimensions of space. Progress in understanding the physical applications crucially depends on a better understanding of spaces, especially singular ones, with exceptional holonomy.
Advances in understanding geometric structures associated with exceptional holonomy spaces have often required insights from apparently disparate parts of the field, or from outside the field entirely. This collaboration brings together the leading mathematics researchers in the various geometric incarnations of exceptional holonomy with experts on the applications to physics. We will capitalize on several recent mathematical breakthroughs related to the geometric structures associated with exceptional holonomy spaces and also make use of powerful, new tools for analyzing singular spaces.
More information about the collaboration can be found here.
The Simons Foundation will support more collaborations in future years; groups interested in applying should review the Request for Applications available on our website.