Colloquium| Institute of Mathematical Sciences
Time：14:00-15:00, September 27 Friday
Location：Room S408, IMS
Speaker: Yoshinori Hashimoto, IMS, ShanghaiTech University
Abstract: Finding a canonical Riemannian metric that has special curvature properties is a natural and important question in differential geometry, and often amounts to solving a nonlinear PDE. A mantra propounded by Atiyah-Bott, Fujiki, and Donaldson states that the curvature of smooth complex projective varieties is an infinite dimensional moment map, and hence canonical metrics can be formulated as a zero of a moment map. On the other hand, the Kempf-Ness theorem states that a zero of a moment map is stable in the sense of Geometric Invariant Theory, indicating a connection between canonical metrics and stability notions in algebraic geometry. This colloquium talk aims to be an informal survey of this area of research, highlighting the role played by a complex analytic object called the Bergman kernel and heavily biased towards the work that I have done. Part of the results presented in this talk is based on a joint work with Julien Keller.