The history of automorphic forms and the role of the uniformization theorem
季理真,1984年获杭州大学理学学士学位,1987年在加州大学圣地亚哥分校获得理学硕士学位,1991年在美国东北大学获得理学博士学位。先后在美国麻省理工学院,普林斯顿高等研究院从事研究工作,1995年至今任教于美国密歇根大学数学系。出版学术著作40余部,并任多个国际学术期刊的主编、编委,以及多部系列丛书的主编。曾组织过多场国际大型学术会议,先后获得P. Sloan研究奖,美国自然科学基金会数学科学博士后奖,晨兴数学银奖, 西蒙斯奖。
季理真教授的研究领域主要是几何、拓扑及数论的交叉融合。他在局部对称空间的紧化、黎曼面的谱、迹公式等方面取得了国际一流的原始创新成就,并在国际一流数学杂志上发表了大量学术论文。他解决了Borel猜想、Siegel猜想等几个长期悬而未决的国际著名猜想,还对另外几个著名的猜想做出了重要贡献,其中包括Novikov猜想。近年来,对近现代数学史产生了浓厚的兴趣。
Automorphic forms are central to contemporary mathematics, playing a pivotal role in both algebraic and analytic number theory. The celebrated Langlands program, for instance, explores their properties on general Lie groups, revealing deep connections between representation theory, arithmetic geometry, and L-functions. These objects generalize automorphic functions, which extend familiar periodic functions such as sinx and cosx, and have profound applications, from the proof of Fermat's Last Theorem to the study of the Riemann Hypothesis. In this talk, we will trace the historical development of automorphic forms, beginning with classical modular forms for SL(2,Z). We will then discuss how Klein and Poincaré's work on the uniformization theorem of Riemann surfaces led to broader notions of automorphic functions and forms, paving the way for modern developments. Through this historical lens, we will examine the interplay between number theory, algebra, analysis, and geometry, highlighting the enduring significance of automorphic forms and their unifying role across diverse areas of mathematics.