Since Donaldson-Thomas proposed a programme for studying gauge theory in higher dimensions, there has been significant interest in understanding special Yang-Mills connections in Ricci-flat 7-manifolds with holonomy G_2 called G_2-instantons.  However, still relatively little is known about these connections, so we begin the systematic study of G_2-instantons in the SU(2) ^{^ 2}-invariant setting.  We provide existence, non-existence and classification results, and exhibit explicit sequences of G_2-instantons where “bubbling" and "removable singularity" phenomena occur in the limit.  This is joint work with Goncalo Oliveira (Duke).

AaDAG seminar:   Aa rhus  D ifferential  A lgebraic  G eometry seminar