Daniel Fadel, Peking University
"Asymptotics of finite energy monopoles on AC 3-manifolds"
I will report on work in progress on sharp decay estimates for critical points of the SU(2) Yang-Mills-Higgs energy functional on asymptotically conical (AC) 3-manifolds, generalizing classical results of Taubes. In particular, I will explain how to prove the quadratic decay estimate of the energy density of any critical point in this general context, combining Bochner formulas with certain refined Kato inequalities with "error terms" and standard elliptic techniques. We deduce that every irreducible finite energy monopole converges along the conical end to a limiting configuration at infinity consisting of a reducible Yang-Mills connection and a parallel Higgs field. If time permits, I will mention a few open problems and future directions in this theory.
This seminar will be held jointly online and in person:
- Zoom link: https://zoom.us/j/93859138328; Passcode: 436044
- Room: MC 5417