报告题目：The Uniformization Theorem: History, Proofs, and Lasting Impacts
报告人：季理真 教授（美国密歇根大学）
会议时间：2025年6月13日 15:00开始
会议地点：色情网
113报告厅
摘要：The uniformization theorem is one of the most significant results in mathematics, with a deceptively simple statement familiar to many: every simply connected Riemann surface is biholomorphic to one of three standard surfaces—the Riemann sphere, the complex plane, or the open unit disk. This theorem has profound extensions to higher dimensions, including Thurston’s geometrization program and, notably, the resolution of the Poincaré conjecture. It is no wonder that this theorem is one of the most important theorems, if not the most important theorem, in the last 150 years. However, its rich history and far-reaching impacts are often underappreciated. For example, the initial formulations and attempted proofs by Klein and Poincaré using the method of continuity introduced many original ideas that have not been fully explored. Later, Teichmüller’s innovative use of the method of continuity played a crucial role in his revolutionary work on Teichmüller space, profoundly influencing the study of moduli spaces of Riemann surfaces. Yet, this deep historical and conceptual connection is frequently overlooked.
In this talk, I will trace the historical development of the uniformization theorem, from its early formulations to its lasting influence across mathematics. I will explore its connections to seemingly unrelated results and modern mathematical areas, particularly in Teichmüller theory and moduli spaces. Through this exploration, I aim to shed light on the theorem’s profound influence, inspire new perspectives on its unifying role in contemporary mathematics.
报告人简介：季理真，美国密歇根大学数学系教授，浙江温州人，1984年获杭州大学（现浙江大学）理学学士， 1985年赴美国在丘成桐教授指导下研习数学，1987年在加州大学圣地亚哥分校获理学硕士学位， 1991年在美国东北大学获理学博士学位。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。曾获得Sloan研究奖，晨兴数学奖银奖西蒙斯奖，以及美国自然科学基金会数学科学博士后奖。
