Ákos Nagy, UC Santa Barbara

Title: The asymptotic geometry of G2-monopoles

Abstract: G2-monopoles are special solutions to the Yang-Mills-Higgs equation on G2-manifolds, similar to 3-dimensional BPS monopoles. Donaldson and Segal conjectured that these gauge theoretic objects have a close relationship to the geometry of the underlying G2-structure. Intuitively, G2-monopoles with "large mass" are predicted to detect coassociative submanifolds.

One of the first steps in proving this claim is understanding the analytic behavior of G2-monopoles. In this talk, I will first introduce the proper analytic setup for the problem. Then I present results about the asymptotic form of G2-monopoles with structure group SU(2) on Asymptotically Conical manifolds. These are joint results with Gonçalo Oliveira and Daniel Fadel. Finally, I will also talk about further plans in this project, in particular:

(1) Generalizations of these results to manifolds with fibered end and higher rank gauge groups.

(2) Glue-in construction of monopoles.

(3) A concentration result for G2-monopoles with large mass.

These are ongoing research directions with Gonçalo Oliveira, Daniel Fadel, and Saman Habibi Esfahani.