## Geometry and Topology

•  Ákos Nagy, Duke University
•  The Asymptotic Geometry of G_2 monopoles
•  02/13/2020
•  2:30 PM - 3:30 PM
•  C304 Wells Hall

G_2 monopoles are special solutions of the Yang-Mills-Higgs equation on G_2 manifolds, and Donaldson and Segal conjectures that one can construct invariants of noncompact G_2 manifolds by counting G_2 monopoles. One of the first steps of achieving this goal is understanding the analytic behavior of these monopoles. In this talk, I introduce the proper analytic setup for the problem, and present our results about the asymptotic form of G_2 monopoles on Asymptotically Conical manifolds with structure group being SU(2). If time permits, I also talk about our further plans in this project, in particular: 1. Generalizations of these results to manifolds with fibered end and higher rank gauge groups. 2. A glue-in construction of monopoles with large mass''. This is a join project with Goncalo Oliveira (UFF, Brazil).

## Contact

Department of Mathematics
Michigan State University