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S. Donaldson - Boundary value problems for $G_2$ structures

In the lecture we consider the existence of G2 structures on 7-manifolds with boundary, with prescribed data on the boundary. In the first part we will review general background and theory, including Hitchin’s variational approach. We will then discuss in more detail reductions of the problem in the presence of symmetry and in ”adiabatic limits”, and connections with real and complex Monge-Ampère equations.
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