题 目：Some Recent Development in Conformal Geometry
报告人:Sun-Yung Alice Chang 教授（普林斯顿大学）
时 间: 2026年3月27日（周五）16:00
地 点: 鼓楼校区西大楼308
报告摘要:This will a survey talk of some recent development in conformal geometry. In this talk, conformal refers to the "angle preserving" property. In a Riemannian manifold M with a metric g, the conformal class [g] of g denotes the module space of such metrics ĝ=p2g by smooth functions p in M. One of the main goal in conformal geometry is to study geometric quantities which are invariant in [g] in either pointwise or integral sense together with their geometric and topological implications. In the talk, topics I will cover include:
Fractional GJMS operators introduced by Graham-Zworski on boundary of asymptotic hyperbolic manifolds via the scattering theory. Among the class of non-local conformal invariants thus introduced, I will report recent progress made on the study of "Renormalized Volume".
As another application, Iwill also report on progress made on a related problem of finding "conformal flling in" in ADS/CFT theory. Given a manifold (Mn,h), when is it the boundary of a conformally compact Einstein manifold (Xn+1,g), in the sense that there exists some defining function p on X so that p2g is compact on the closure of X and p2g restricted to M is the given metric h? The model example is the n-sphere as the conformal infinity of the hyperbolic (n+1) ball. I will discuss the compactness, existence and uniqueness aspects of the problem.
报告人介绍:
张圣容（Sun-Yung Alice Chang）Princeton大学Eugene Higgins讲座教授，美国科学院院士，美国艺术与科学院院士，台湾“中央研究院”院士，瑞典皇家科学院外籍院士，ICM受邀报告人（45分钟报告-1986 Berkeley；1小时报告-2002 Bejing；ICM Emmy Noether Lecture-2018 Rio)，美国女数学家协会会员等。张圣容教授1970年在台湾国立大学获学士学位，1974年在UC Berkeley获博士学位。她曾任UCLA与UC Berkeley教授。她是一位几何分析领域中的卓越学者。她的学术生涯从研究经典调和分析中的问题开始，逐渐地她的研究兴趣不断扩展至其他领域包括共形几何与非线性偏微分方程交叉方向。她因其卓越的学术成就获得许多奖项：Sloan奖，美国数学会Scatter Prize，Guggenheim Fellow，MSRI Simons讲座教授，Pierre and Marie Curie大学荣誉博士等。
