Rigidity of positive scalar curvature

Thomas Schick   (University of Göttingen)

13:30-14:30, July 13, 2026   闵行校区数学楼 102

Abstract:

We discuss a classical problem in global Riemannian geometry: Loosely speaking, it asks: "how round can one make a given manifold"? More concretely: if one avoids the obvious scaling trick: given a metric g with non-negative scalar curvature on a smooth manifold M, can one find g' such that distances are not decreased when measured with g' instaed of g, but such that the scalar curvature increases? A classical result by Llarull states that this is not the case if g is the round metric on the sphere S^n (n>1); Goette and Semmelmann generalize this to further classes of manifolds, in particular symmetric spaces of compact type with non-vanishing Euler characteristic. We discuss the possible approaches to study this question and a number of important generalizations/variations: a) the condition is purely metric: therefore also the conclusion should hold under low assumptions on the regularity (this is joint work with Simone Cecchini, Bernhard Hanke, Lukas Schoenlinner b) certain instances where the manifold has Euler characteristic zero (but is not a sphere): this is joint work with Georg Frenck, Lukas Schoenlinner, Thomas Tony

About the speaker:

Thomas Schick 教授现任德国哥廷根大学（University of Göttingen）数学系教授、哥廷根科学院院士，是代数拓扑与非交换几 何领域的国际顶尖学者。他在指数理论、粗几何、K-理论、B aum-Connes 猜想以及流形正标量曲率刚性等领域做出了众多 开创性和基础性的贡献。凭借其卓越的学术成就，Schick 教授 曾受邀在国际数学家大会（ICM）上作邀请报告。其多项重量 级研究成果发表在 Journal of the American Mathematical Society、Inventiones mathematicae 、Geometry & Topology 等一流数学期刊上。

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