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BIMSA General Relativity Seminar
Adiabatic approximation of Abelian Higgs model in dimension
Adiabatic approximation of Abelian Higgs model in dimension
演讲者
时间
2024年09月30日 15:30 至 17:00
地点
A3-2-301
线上
Zoom 559 700 6085
(BIMSA)
摘要
In this talk, I will present my PhD thesis about the approximation of the Abelian Yang-Mills-Higgs equation by wave maps. These equations describe the interaction of the Higgs field and the electromagnetic field. They have gauge symmetries and are hyperbolic. At the critical coupling, the finite energy and static solutions in dimension have been classified by Jaffe and Taubes in 1980, the so called (anti)-vortex configurations and they form a moduli space which is a smooth Riemannian manifold. In this talk I will explain that one can find adiabatic solutions in dimension whose dynamics are approximated by wave maps to the moduli space, a generalization of the geodesic approximation in dimension which has been proved by Stuart in 1994. We use the gluing method to construct solutions and take advantage of the so called Higgs mechanism, the existence of a spectral gap for the linearization of the equations, under specific gauge conditions. This is a joint work with Robert Jerrard.