一、报告题目

Uniformization of metric surfaces of finite area

二、主讲人

Dimitrios Ntalampekos（纽约州立大学石溪分校助理教授）

三、报告时间

2023年10月9日 20:00-21:00

四、报告地点

Zooms会议

五、摘要

The classical uniformization theorem for Riemann surfaces implies that every smooth two-dimensional sphere can be conformally parametrized by the Euclidean sphere. The recent developments in the field of Analysis on Metric Spaces have allowed the extension of this result beyond the smooth setting. Sufficient geometric conditions have been established so that a fractal sphere can be transformed to the Euclidean sphere with a bi-Lipschitz, quasisymmetric, or quasiconformal map. The milestones in this direction are the works of Bonk-Kleiner on the quasisymmetric uniformization of spheres and of Rajala on the characterization of quasiconformal spheres. It was conjectured by Rajala and Wenger that, under no assumption, every metric two-dimensional sphere of finite area can be parametrized by the Euclidean sphere with a weakly quasiconformal map. In this talk we present an affirmative answer to this conjecture.

六、主讲人简介

Dimitrios Ntalampekos，2018年博士毕业于美国加州大学洛杉矶分校(UCLA)，师从著名数学家Mario Bonk教授，现为纽约州立大学石溪分校助理教授。主要研究方向为复分析和度量空间上的分析，在度量空间的单值化理论和刚性理论方面做出了重要贡献，在Invent. Math., Duke Math. J., Amer. J. Math., Adv. Math., Tran. Amer. Math. Soc., Proc. Lond. Math. Soc., Math. Ann., Arch. Ration. Mech. Anal., J. Lond. Math. Soc.等国际期刊发表论文近20篇。

七、主办单位

非线性期望前沿科学中心

数学与交叉科学研究中心

中俄数学中心青岛基地