Contractions of Lie groups, representations and the Mackey bijection

：Nigel Higson（Pennsylvania State University，US）
：2022-07-08 09:00
：腾讯会议ID：424-451-650（无密码）

报告人：Nigel Higson（Pennsylvania State University，US）

时  间：7月8日上午09:00

地  点：腾讯会议ID：424-451-650（无密码）

内容摘要:

The contraction of a Lie group to a closed subgroup is a Lie group that approximates the larger group to first order near the subgroup. The terminology comes from mathematical physics, where the group of Galilean transformations may be viewed as a contraction of the group of Lorentz transformations. In geometry, the group of isometries of Euclidean space may be viewed as a contraction of the group of isometries of hyperbolic space. It is natural to guess that there is a limiting relationship between representations of the contraction group and representations of the original group. But in the 1970’s George Mackey conjectured an interesting rigidity phenomenon: in the case of a maximal compact subgroup of a semisimple group, instead of a limiting relationship there is an exact bijection. I shall tell the story of how this conjecture was made precise and eventually resolved. Among other things, C*-algebra theory and topology played important roles. However, although the proof is now complete, a conceptual explanation for Mackey’s rigidity phenomenon remains elusive.

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.

 

联系人：余世霖