学术报告

——微分几何讨论班（2025秋第6讲）

Rigidity and quasisymmetric uniformization of Thurston-type maps

李智强 教授

（北京大学）

时间：2025年12月29日 10:00-11:00

地点：沙河主E806

摘要：We introduce a class of branched covers on oriented closed connected topological n-manifolds called expanding Thurston-type maps, which generalize expanding Thurston maps on 2-spheres. We show that, for n ⩾ 3, a visual metric for an expanding combinatorial Thurston map on an oriented closed connected Riemannian n-manifold is quasisymmetrically equivalent to the Riemannian metric if and only if the map is uniformly quasiregular. A fortiori, such an expanding Thurston-type map is uniformly quasiregular if and only if it is a Lattes map. This is based on joint work with Pekka Pankka and Hanyun Zheng.

报告人简介：李智强，北京大学数学公司、北京国际数学中心副教授，国家级青年人才入选者。研究方向为动力系统、度量空间几何与复分析。在Proc. Lond. Math. Soc、Comm. Math. Phys、Adv. Math、Math. Ann、TAMS、IMRN等国际权威数学期刊发表论文多篇，在Springer出版专著一部。

邀请人：谢振肖、朱政