Chengjian Yao

(ShanghaiTech)

15:00-16:00

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.

Venue: https://zoom.us/j/97776574795

Kai Zheng

(Tongji)

16:00-17:00

Title: Some estimates on extremal metrics

Abstract: In this talk, we will present a compactness theorem on extremal metrics.

Venue: https://zoom.us/j/94697225681

Long Li

(ShanghaiTech)

15:15-16:15

Title: Approximation of the geodesic and the affine Mabuchi functional

Abstract: tba

Venue: https://zoom.us/j/98855180589

Wei Sun

(ShanghaiTech)

16:15-17:15

Title：Interior gradient estimates for prescribed curvature equation

Abstract: In this talk, we shall talk on interior gradient estimates for admissible solutions to prescribed curvature equations.

Venue: https://zoom.us/j/97914203553