报告题目：Generalized Ginzburg–Landau equations in high dimensions
报告摘要：In this talk, we present some results on critical points of the generalized Ginzburg–Landau equations in dimensions n ≥ 3 which satisfy a suitable energy bound, but are not necessarily energy-minimizers. When the parameter in the equations tends to zero, such solutions are shown to converge to singular n-harmonic maps into spheres, and the convergence is strong away from a finite set consisting (1) of the infinite energy singularities of the limiting map, and (2) of points where bubbling off of finite energy n-harmonic maps could take place. The latter case is specific to dimensions >2. We also exhibit a criticality condition satisfied by the limiting n-harmonic maps which constrains the location of the infinite energy singularities. Finally we construct an example of on-minimizing solutions to the generalized Ginzburg–Landau equations satisfying our assumptions.