International Workshop on
Special Geometry and Minimal Submanifolds

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   Jason Lotay (Univ. College London)
   
Title : Stability, conifolds and G2 geometry   
 Abstract

 Conifolds are manifolds which have asymptotically conical ends or have conical singularities. In the context of G_2 geometry, key geometric questions for conifolds are intimately related to the spectrum of an elliptic operator on the cross-section of the cone. From this spectrum, based on the pioneering work of Joyce, one is led to define an integer invariant associated with the cone called the stability index. I will describe the connections that the stability index has to various problems for conifolds, with an especial focus on coassociative submanifolds in 7-manifolds with G_2 holonomy, including: deformation theory, gluing problems and existence and uniqueness questions.




 
   
 
Organizer: Reiko Miyaoka
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 Grants-in-Aids for Scientific research:23340012