國立清華大學 數學系

Abstract: In this talk, I will survey the recent developments of the elliptic system arising from the Chern-Simons Model with two Higgs Particles. Mathematically, the system is a typical skew-symmetric system. Thus, the action functional of this system is indefinite, which makes it difficult to study from the variational method. Among others, I will present my recent works on this system, including the uniqueness of the topological solutions and the radial non-topological solutions, existence of bubbling solutions on a torus and the sharp estimates on the fully bubbling solutions of Liouville type (joint work with X. Han and C.S. Lin, Y.Lee and L. Zhang).