以表彰他在代數、代數幾何和表示論方面作出了基礎性的貢獻,並將這些學科結合起來,解決古典問題,且展現數學中美妙的新聯繫。
2014年度邵逸夫數學科學獎頒予喬治・盧斯蒂格 (George Lusztig),他是美國麻省理工學院Abdun-Nur數學講座教授。他在代數、代數幾何和表示論方面作出了基礎性的貢獻,並將這些學科結合起來,解決古典問題,且展現數學中美妙的新聯繫。
兩百多年以來,對稱群一直處在數學及數學應用的中心位置,如十九世紀初,傅立葉在熱傳導方程的工作;二十世紀初魏爾在量子力學的工作;以及由阿廷和舍瓦萊創立的數論方法。這些經典工作顯示,幾乎任何關於對稱群的問題,其答案可以從對稱群的矩陣實現去尋找,即借助於對稱群的表示。
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.