Title: Extremal metrics on toric manifolds and Related problem

Speaker: Li Sheng (Sichuan University)

Abstract: In a sequence of papers, Donaldson initiated a program to study the extremal metrics on toric manifolds and solved the problem for cscK metrics on toric surfaces. For toric manifolds, the equation of extremal metrics can be reduced to a real 4th-order partial differential equation on the Delzant polytope, called the Abreu equation.

In joint papers with Li An-Min and Chen Bohui we apply the affine techniques to extend the existence result in dimension 2 to extremal metrics. In joint work with Chen Bohui, Han Qing, Li An-Min and Lian Zhao, we study generalized Abreu equations on a Delzant ploytope and use the similar method to study constant scalar curvatures on homogeneous toric bundles.

Time/Venue: 2019.2.24  10:00-11:00  B924