学术报告通知

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

报告人：Professor Matti Vuorinen (Turku University)

报告时间: 2019年11月10日（周日）下午4：00-5：00

报告地点：工程设计学院306

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 quasi-hyperbolic, modulus, Apollonian, Mobius and generalized hyperbolic metrics, resp. Here we discuss a new hyperbolic type metric and give an application to quasiconformal maps.

报告人简介： Matti Vuorinen教授是芬兰大学赫尔辛基以及图尔库大学的著名教授，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。迄今出版学术专著两本，发表学术论文两百余篇。