Gravitating Vortices with positive curvature on Riemann sphere

时间:2019-11-26

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.


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