Speaker：Nigel Higson（Pennsylvania State University，US）

Time：2022-07-08, 09:00

Location：Tencent Meeting ID：424-451-650（No Password）

Abstract:

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.