以表彰他在代数、代数几何和表示论方面作出了基础性的贡献,并将这些学科结合起来,解决古典问题,且展现数学中美妙的新联系。
2014年度邵逸夫数学科学奖颁予乔治・卢斯蒂格 (George Lusztig),他是美国麻省理工学院Abdun-Nur数学讲座教授。他在代数、代数几何和表示论方面作出了基础性的贡献,并将这些学科结合起来,解决古典问题,且展现数学中美妙的新联系。
两百多年以来,对称群一直处在数学及数学应用的中心位置,如十九世纪初,傅立叶在热传导方程的工作;二十世纪初魏尔在量子力学的工作;以及由阿廷和舍瓦莱创立的数论方法。这些经典工作显示,几乎任何关於对称群的问题,其答案可以从对称群的矩阵实现去寻找,即借助於对称群的表示。
For more than two hundred years, symmetry groups have been at the centre of mathematics and its applications: in Fourier’s work on the heat equation in the early 1800s; in the work of Weyl and Wigner on quantum mechanics in the early 1900s; and in the approach to number theory created by Artin and Chevalley. These classical works show that answers to almost any question involving a symmetry group lie in understanding its realizations as a group of linear transformations, that is, in terms of its representations.
Lusztig’s work has completely transformed our understanding of representation theory, providing complete and precise answers to fundamental questions that were understood before only in very special cases. What he has done has advanced all of the mathematics where symmetry groups play a role: from Langlands’ programme for understanding automorphic forms in number theory, to classical problems of harmonic analysis on real Lie groups.