Title: Gravitating Vortices with positive curvature on Riemann sphere

Speaker：Yao Chenjian， ShanghaiTech University

Time: 2019-12-6, 16:00-17:30

Place: Room 5206, The 5th Teaching Building, East Campus

Abstract：Gravitating vortex equation is a system of PDEs coupling constant scalar curvature problem and Hermitian-Yang-Mills problem on a line bundle on a Riemann surface in the presence of a Higgs field. We prove that gravitating vortex equation on P^1 with positive curvature is solvable if and only if the divisor, i.e. the zeros of the Higgs field, is polystable under the canonical SL(2,C)-action. Our method uses a continuity path starting from Yisong Yang's solution with zero curvature (in relation to some gravitating problem in theoretical physics) and deforming the coupling constant towards 0. This is a joint work with Mario Garcia-Fernandez and Vamsi Pingali.