Geometry & Topology Seminar

Vasileos (Hector) Papoulias, Oxford University

"Spin(7) Instantons and HYM Connections on Asymptotically Conical Calabi-Yau Fourfolds"

The Spin(7) and SU(4) structures on a Calabi-Yau (CY) fourfold give rise to certain first order PDEs defining special Yang-Mills connections: the Spin(7) instanton equations and the Hermitian Yang-Mills (HYM) equations respectively. The latter are stronger than the former. In 1998 C. Lewis proved that -over a compact base- the existence of an HYM connection implies the converse establishing equivalence.

In this talk we present recent progress on the relationship between the two equation systems in the asymptotically conical (AC) setting. We extend Lewis’s argument under assumptions on the asymptotic decay rate and construct a counterexample demonstrating that these assumptions cannot be relaxed. In doing so, we construct the full moduli space of SO(5) invariant Spin(7) instantons over the Stenzel manifold. These are the first examples of pure (non-HYM) Spin(7) instantons coexisting with HYM solutions - a phenomenon precluded in the compact world by Lewis's original argument. This paves the way to higher resolution questions regarding the relationship between the two systems. The aforementioned moduli space exhibits a curious removable singularity/ bubbling phenomenon that might prove a first step in this direction.

This seminar will be held jointly online and in person:

• Zoom link: https://zoom.us/j/93859138328; Passcode: 436044
• Room: MC 5417