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- The mathematics of G_2 conifolds for M-theory

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13100126

G_2 manifolds play

the analogous role in M-theory that Calabi-Yau manifolds play in string

theory. There has been work in the physics community on conjectural

"mirror symmetry" in this context, and it has also been observed that

singularities are necessary for a satisfactory theory. After a very

brief review of these physical developments (by a mathematician who

doesn't necessarily understand the physics), I will give a mathematical

introduction to G_2 conifolds. I will then proceed to give a detailed

survey of recent mathematical developments on G_2 conifolds, including

desingularization, deformation theory, and possible constructions of G_2

conifolds. This includes separate joint works of myself with Jason

Lotay and with Dominic Joyce.

©2012 Perimeter Institute for Theoretical Physics