Mathematical Sciences: Minimal K-types and Hecke Algebra Isomorphisms for p-adic Groups

李群理论是为了纪念挪威数学家索夫斯·李而命名的，它一直是20世纪数学的主要主题之一。作为探索系统中固有对称性的数学工具，李理论对数学本身和理论物理，特别是量子力学和基本粒子物理产生了深远的影响。李论的一个主要应用是代数数论，对p进理论的理解是必不可少的。梅教授可能是这个领域最优秀的年轻研究员。他最近关于最小k型和Hecke同构的研究为p进群的表示理论提供了一些长期以来最重要的进展。梅计划继续发展这一理论。他提出的工作将现实理论的最新结果推广到p进情况。梅教授设想将其应用于关键的离散系列表示。

The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, Lie theory has had a profound impact upon mathematics itself and theoretical physics, especially quantum mechanics and elementary particle physics. A major application of Lie thoery is to algebraic number theory, for which an understanding of the p-adic theory is essential. Professor Moy is possibly the strongest young researcher in this area. His recent work on minimal K-types and Hecke isomorphism provides some of the most important advances in the representation theory of p-adic groups in a long time. Moy plans to continue the development of this theory. His proposed work generalizes the most current results from the real theory to the p-adic case. Professor Moy envisages application to the crucial discrete series of representations.