Nigel Higson教授受邀做天元名家讲堂

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78日上午,应国家天元数学东南中心与数学科学学院邀请,美国宾夕法尼亚州立大学Nigel Higson教授线上为我院师生做了题为《Contractions of Lie groups, representations and the Mackey bijection》的天元名家讲堂。

讲座由厦门大学数学科学学院余世霖教授主持。数学科学学院副院长朱玉峻教授代表厦门大学数学科学学院和国家天元数学东南中心致辞,向Nigel Higson教授做客名家讲堂表示欢迎及感谢,并诚挚邀请Nigel Higson教授待疫情好转时来厦门大学交流指导。

Nigel Higson教授受邀做天元名家讲堂

本次讲座中,Nigel Higson教授向我们介绍了李群到其闭子群的收缩及相关问题。李群的收缩是李群到其闭子群的一阶近似,该术语来自数学物理,经典的例子是伽利略变换群可被视为洛伦兹变换群的收缩。上世纪七十年代,George Mackey 提出了一个有趣的刚性猜想:半单群和其到最大紧子群的收缩的表示之间可能存在一个特别的双射。Nigel Higson教授向我们讲述了这个猜想是如何被精确化并最终得到解决的。其中,C*-代数理论和拓扑学发挥了重要作用。然而,尽管现在证明已经完成,依然缺乏对 Mackey 刚性现象的概念性解释。Nigel Higson教授向我们介绍了他与合作者在复约化群情形下利用C*-代数对Mackey双射给出的新证明。讲座结束后,Nigel Higson教授与听众就细节进行了深入探讨。

个人简介:Nigel HIGSON’s research specialty is operator algebra theory, a subject with roots in the mathematical foundations of quantum theory and in Fourier analysis. Professor Higson's recent work has focused on the Baum-Connes conjecture—a broad program which connects operator algebra theory to problems in differential topology, Riemannian geometry—and on various areas of group representation theory. Along with Paul Baum (a colleague at Penn State) and Alain Connes (Collège de France), Higson is responsible for the current form of the Baum-Connes conjecture.

Professor Higson's research accomplishments have been regularly recognized, both nationally and internationally. He was awarded a Sloan Fellowship and won Canada's Aisenstadt Medal and its Coxeter-James and Halperin Prizes, all of which recognize young mathematicians who have made outstanding contributions to mathematical research. He has delivered plenary addresses to the American, Australian and Canadian Mathematical Societies, and in 1998 he delivered an invited lecture to the International Congress of Mathematicians in Berlin. In 1998 he was named a Clay Mathematics Institute Prize Fellow. He delivered the DeLong lectures at the University of Colorado in 1999; the Namboodiri lectures at the University of Chicago in 2008, the Plücker lectures at the University of Bonn in 2014; and the Kemeny Lectures at Dartmouth College in 2020. He was named a Fellow of the Royal Society of Canada in 2000 and an Inaugural Fellow of the American Mathematical Society in 2012. He has held visiting positions as the Stanislaw Ulam Professor, University of Colorado, 1996; as a Distinguished Visiting Professor at Kyoto University, 2017; and as an Excellence Initiative Professor at Radboud University, 2022.