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Title:
Codimension one collapse and special holonomy metrics
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Abstract:
In this talk we describe recent developments related to codimension one collapse of exceptional holonomy metrics. i.e. where a family of special holonomy metrics on a space of dimension n converges in some limit to a metric on a space of dimension n-1. Interesting examples occur for hyperkaehler 4-manifolds, G_2 holonomy manifolds and Spin_7 holonomy manifolds. The talk will focus on the G_2 holonomy case, but will also draw on the better understood hyperkaehler case for inspiration and for useful analogies. These mathematical developments are closely related to important limits in physics, e.g. in the context of G_2 holonomy metrics it is related to the identification of the weak coupling limit of M theory compactified on a G_2 holonomy space being Type IIA String Theory on a 6-dimensional space. This is work joint with Lorenzo Foscolo and Johannes Nordstr\”om.
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