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Title:
G2–instantons over twisted connected sums
Speaker:
Abstract:
Donaldson and Thomas’s visonary article “Gauge Theory in Higher Dimensions” initiated a program to study gauge theory in the context of special holonomy and, in particular, on G2–manifolds. I will explain how the quest for a higher dimensional version of Chern–Simons theory naturally leads to G2–geometry. In joint work with H. Sá Earp, we introduced a method to construct G2–instantons over compact G2–manifolds arising as the twisted connected sum (TCS) of a matching pair of building blocks. After reviewing the TCS, I will discuss our main result and explain how to interpret it in terms of certain Lagrangian subspaces of a moduli space of stable bundles on a K3 surface. Finally, I will talk about how to use our construction to produce a rather concrete example of a G2–instanton over twisted connected sum discovered by Crowley and Nordström. Time permitting, I will also discuss ideas for implementing Mukai duality for TCS G2–manifolds (currently being investigated in joint work with A. Kovalev).
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