Geometry and Physics of G2 Manifold

Part of the Long Program Symplectic Geometry and Physics
April 29 - May 2, 2003

Overview

Seven dimensional manifolds with holonomy group G2 are always Einstein manifolds. Examples of them are constructed by Bryant, Salamon, Joyce, Kovalev and others. Even though we expect to have a lot of them, a general existence theorem is still lacking. G2 geometry can be interpreted as oriented octonion geomery (Lee and Leung). It has natural classes of calibrated submanifolds (Harvey and Lawson) and Yang-Mills bundles (Donaldson and Thomas). In M-theory, G2 manifolds play an important role, similar to the role of Calabi-Yau threefolds in String theory. There are many duality transformations for them. In particular Calabi-Yau 3-folds with D-branes are equivalent to M-theory backgrounds with G2 holonomy (Atiyah, Maldacena, Vafa). In this context G2 flop can be used to explain Large N dualities. Mirror symmetry in the context of G2 is very interesting to study in the context of T-duality (Acharya, Gukov-Yau-Zaslow, Aganagic-Vafa). This workshop aims at exploring the various aspects of G2 manifolds. Among the topics to be explored are:

  •     Constructions of manifolds with exceptional holonomy.
  •     Minimal submanifolds and Yang-Mills bundles on G2 manifolds.
  •     M-theory
  •     Duality transformations.

 

Organizing Committee

Huai-Dong Cao (IPAM)
Naichung Conan Leung (University of Minnesota, Twin Cities, Mathematics)
Cumrun Vafa (Harvard University, Physics)
Shing-Tung Yau (Harvard University, Mathematics)