Seminar| Institute of Mathematical Sciences
Time：15:00-16:00, October 28 Wednesday
Location：Room 408, IMS
Speaker: Chengjian Yao, Assistant Professor，IMS, ShanghaiTech University
Title: Gravitating vortices and cosmic strings with singularities
Abstract: We introduce the notion of twisted gravitating vortices on a compact Riemann surface. If the genus of the Riemann surface is greater than 1 and the twisting forms have suitable signs, we prove an existence and uniqueness result for suitable range of the coupling constant. It is proved via solving a continuity path deforming the coupling constant from 0 for which the system decouples as twisted Kahler-Einstein metric and twisted vortices. Moreover, specializing to a family of twisting forms smoothing delta distribution terms, we prove the existence of singular gravitating vortices whose Kahler metric has conical singularities and Hermitian metric has parabolic singularities. In the Bogomol'nyi phase, we establish an existence result for singular Einstein-Bogomol'nyi equations, which represents cosmic strings with singularities.