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G_{2}-manifolds with boundary

Simon Donaldson (Imperial College and Simons Center for Geometry and Physics)

Location:  Hill 705
Date & time: Tuesday, 06 March 2018 at 4:00PM - 5:00PM

Abstract:  The first part of the talk will be general background on 7-dimensional Riemannian manifolds with the exceptional holonomy group \(G_{2}\), going back to Berger's classification from the 1950's.  Then we will explain that there is a natural boundary value problem for these structures, involving fixing a 3-form on the boundary, and discuss some of the existence questions that arise. We will consider various reductions of the equations, imposing symmetry, to lower dimensions which lead to interesting PDE problems---some of which are familiar  and some new. 


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