Noncommutative geometry of the Satake compactification

Nigel Higson  (Penn State University)

9:30-10:30, May 18 - May 21, 2026, each day   Wenfu Building 502

Abstract:

My lectures will be about the construction of a new groupoid in Lie theory,about the noncommutative geometric aspects of this groupoid, and about applications, real and potential, to representation theory. This is joint work with Jacob Bradd and Robert Yuncken. The (maximal) Satake compactification associated to a real reductive group G is the closure of the symmetric space of all maximal compact subgroups within the compact space of all closed subgroups of G. I shall present different views of a groupoid that may be associated to the Satake compactification. The general idea behind this Satake groupoid is due to Omar Mohsen. But I shall give a Lie-theoretic account of Mohsen’s construction, and I shall also identify the groupoid with a purely geometric construction arising from Richard Melrose’s b-calculus. Turning to applications, I shall give a geometric account, using the groupoid, of Harish-Chandra’s principle that a tempered irreducible representation of a real reductive group is either discrete series, modulo center, or embeddable in a representation that is parabolically induced from such a representation. Time permitting, I shall speculate on potential applications to non-Riemannian symmetric spaces and to Plancherel formulas.

About the speaker:

Nigel Higson 教授现任美国宾夕法尼亚州立大学（Penn State）数学系Evan Pugh大学教授（该校最高学术头衔）。他的研究专长为算子代数理论，其核心工作聚焦于 Baum-Connes 猜想—这是一个将算子代数与微分拓扑、黎曼几何及群表示论深刻联系起来的宏大数学纲 领。Higson 教授与 Paul Baum 以及菲尔兹奖得主 Alain Connes 共同合作，确立了该猜想现今的标准形式，对现代非交换几何的发展做出了奠基性贡献。 Higson 教授的杰出学术成就为他赢得了广泛的国际声誉。他曾荣获斯隆研究奖（Sloan Fellowship）、加拿大 Aisenstadt奖章、Coxeter-James 奖以及克雷数学研究所奖金学者等众多重量级奖项，并先后当选为加拿大皇家学会院士（2000年）及美国数学学会（AMS）首批会士（2012年）。他曾于1998年受邀在柏林国际数学家大（ICM）作邀请报告，并多次受邀在芝加哥大学、波恩大学、京都大学等全球顶尖高校发表重要的冠名系列讲座。

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