Title: Spin(7) Bubbles and Flops under Cohomogeneity-One Assumptions

Abstract:  In this talk, I will discuss geometric transitions and gauge theory on complete noncompact Spin(7) spaces with Aloff–Wallach principal orbits. Cohomogeneity-one symmetry reduces both the torsion-free Spin(7) equations and the invariant gauge theory equations to dynamical systems, providing a setting in which metric degenerations and curvature concentration can be visualised and studied explicitly.
On the gauge-theoretic side, I will describe the construction and moduli problem of invariant Spin(7)-instantons, including a compactification model incorporating both metric and gauge-theoretic bubbles. On the metric side, we will describe three families of asymptotically locally conical metrics, and describe bubble-like behaviour as in the gauge theoretic side. In particular, we will outline how two of the metrics are related by a Spin(7)-flop in the orbifold category, following the expectations of the physicists Cvetic--Gibbons--Lu--Pope and earlier results of Lehmann.
Based on joint work with Hanci Chi.