Gauge theory on G2–manifolds

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• Thomas Walpuski, Imperial College
• Wednesday 12 March 2014, 15:45-16:45
• MR13.

If you have a question about this talk, please contact Ivan Smith.

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In their seminal paper “Gauge theory in higher dimension” Donaldson and Thomas suggested to construct a gauge theoretic enumerative invariant of G2–manifolds, some times called the G2 Casson invariant, by counting G2–instantons and/or associative submanifolds. I will discuss two recent existence results for G2–instantons and a partial converse of Tian’s foundational bubbling analysis. It is a consequence of the latter that the conjectural G2 Casson invariant should be a weighted count of both G2–instantons and associative submanifolds and that the weights have to behave in a very special way. Constructing a coherent system of weights is a difficult open problem. If time permits, I will discuss some ideas for producing such weight systems and the analytical problems involved.

This talk is part of the Differential Geometry and Topology Seminar series.

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