Title: Manifolds with G2 holonomy: associative 3-folds and geometric transitions.
Speaker: Mark Haskins
Speaker Info: Imperial College, London
Manifolds with holonomy G2 are exotic cousins of Calabi-Yau 3-folds; they are very special Ricci-flat 7-manifolds of interest both to geometers and to String/M-theorists. Like Calabi-Yau 3-folds, G2 manifolds admit interesting calibrated submanifolds: associative 3-folds and coassociative 4-folds. Examples of compact G2 manifolds are hard to come by, particularly ones exhibiting interesting associative 3-folds. We construct many new compact G2 manifolds containing rigid associative 3-folds. In many cases we determine the diffeomorphism type of the underlying 7-manifold and show that often the same 7-manifold can be given a holonomy G2 metric in a number of (apparently unrelated) ways; the number of associative 3-folds present in the construction varies accordingly. We show how many of our holonomy G2 manifolds can be related to other holonomy G2 manifolds via a G2 analogue of the "reverse conifold transition".Date: Monday, April 4, 2011
The construction uses a combination of methods: algebraic geometry, complex Monge-Ampere equations on non-compact complex 3-folds and perturbation methods in geometric PDE.