题目：Adiabatic approximation of Abelian Higgs model in dimension (3+1)

报告人：Amirmasoud Geevechi (BIMSA, 清华大学)

时间: 6月3日上午10:00-11:00

地点：二教2605

摘要：In this talk, I will present my Ph.D thesis about the adiabatic 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 U(1) gauge symmetry and are hyperbolic. At the critical coupling, the finite energy and static solutions in dimension 2 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 (3+1) whose dynamics are approximated by wave maps to the moduli space, a generalization of the geodesic approximation in dimension (2+1) 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 project was supervised by Prof. Robert Jerrard.