报告时间：2019年11月9日下午2:30-3:30

报告地点：数学院会议室

报告题目：Conformal Invariants: A Look at Computation and Theory

报告人：芬兰图尔库大学Matti Vuorinen教授

邀请人：李雅湘

报告人简介：Matti Vuorinen教授现为芬兰图尔库大学数学与统计系教授，是拟共形映射、共形不变量和度量空间上的几何与分析等研究领域的国际著名数学家。1980年至2003年，历任芬兰科学院和赫尔辛基大学的高级研究员和研究教授。2000年—2004年曾任诺基亚研究中心的高级科学家。长期担任芬兰数学与逻辑国家研究生院的主席和协调人。为多家国际期刊杂志的编委，为芬兰科学院多个科研项目负责人，曾被许多国际会议和研讨会邀请做学术报告和讲座，曾多次组织复分析、调和映射和拟共形映射等研究领域的大型国际会议，如芬兰--罗马尼亚复分析国际会议、Nevanlinna学术研讨会和2010年国际数学家大学卫星会议等。Vuorinen教授具有广泛的国际合作关系，有来自美国、俄罗斯、中国、印度、日本以及欧洲国家等50多个合作者。迄今出版学术专著两本，主编国际学术会议会刊四本，共发表学术论文近220多篇，被引用2600多次。

报告摘要：Conformal invariants (such as harmonic measure, extremal length, capacity of condensers and hyperbolic metric) are key tools of geometric function theory in the plane. But their application is limited because of lack of explicit formulas. In the cases where formulas exist, they may be challenging to use for paper and pen calculations. In the first part of the talk we report about recent progress in numerical computation of several conformal invariants  in the planar case. Experiments based on this work have led to a number of conjectures, which will be also discussed. In the second part of the talk we discuss efforts, due to many authors, to generalize the hyperbolic metric to R^n, n ≥ 3 . Metrics sharing some (but not all) properties of the hyperbolic metric are called hyperbolic type metrics. Some of these hyperbolic type metrics were introduced by F. W. Gehring, J. Ferrand, A. Beardon, P. Seittenranta, P. Hasto: the quasihyperbolic, modulus, Apollonian, Mobius and generalized hyperbolic metrics, resp. Here we discuss a new hyperbolic type metric and give an application to quasiconformal maps.