Chengjian Yao (ShanghaiTech) will speak in the differential geometry seminar at 2pm on 2nd December, in the Salle des Profs (9th floor building NO). Chengjian’s title is “Geometries of Einstein-Bogomol’nyi equation and Kähler-Yang-Mills equations” and his abstract is below.
The moment map interpretation of the Einstein-Bogomol’nyi equation/self-dual Einstein-Maxwell-Higgs equation on compact Riemann surfaces yields natural obstructions to the existence of solutions, generalizing the Futaki invariant in the constant scalar curvature Kähler metric problem. This point of view also enables us to formulate and show uniqueness of solutions using symplectic reduction by stages. I will also present results on the existence and the structure of moduli space of Einstein-Bogomol’nyi metrics. These results are mainly based on joint works with Alvarez-Consul, Garcia-Fernandez, Garcia-Prada and Pingali in recent years. If time permits, I will also describe some ongoing work with Pingali about the uniqueness of Kähler-Yang-Mills metrics in higher dimensions.