乔治·莫斯托1923—2017

他发现的李群的格的刚性，称为莫斯托刚性。他对刚性的研究，在三位菲尔兹奖得主格列戈里·马尔古利斯、威廉·瑟斯顿、格里戈里·佩雷尔曼的工作中发挥关键作用。

生平

乔治·莫斯托生于1923年。1948年他获得哈佛大学博士学位。他从1952年到1961年在约翰·霍普金斯大学出任第一份主要教职，从1961年起在耶鲁大学担任教授，直至1999年退休。1974年，他获选为美国国家科学院院士。从1982年到1992年，他担任普林斯顿高等研究院的理事。1993年，他因着研究成果及1973年的著作Strong rigidity of locally symmetric spaces，获得美国数学学会Leroy P. Steele重大研究贡献奖。2013年，他获得沃尔夫数学奖。

工作

他发现并研究了半单李群（没有紧致因子群及中心）的格的刚性性质，此处的格即是半单李群的离散子群，使得李群模去离散子群的商空间是紧致的。他的1972年的刚性定理指这些半单李群的格之间的同构，可以扩张至李群之间的解析同构， SL(2,R)/± 1 除外。应用至双曲流形上，得出高于二维的有限体积双曲流形，可以从其基本群确定。（在二维时（紧致黎曼曲面）不成立：每个情况会有多个双曲结构，以泰希米勒空间参数化。）莫斯托的工作激发了对称空间的研究（威廉·瑟斯顿的三维流形分类），并成为类似的刚性定理的范例，例如格列戈里·马尔古利斯基于莫斯托的工作，在1974年证明对秩大于1的半单李群的格的算术性。

George Daniel Mostow (July 4, 1923 – April 4, 2017) was an American mathematician, renowned for his contributions to Lie theory. He was the Henry Ford II (emeritus) Professor of Mathematics at Yale University, a member of the National Academy of Sciences, the 49th president of the American Mathematical Society (1987–1988), and a trustee of the Institute for Advanced Study from 1982 to 1992.

The rigidity phenomenon for lattices in Lie groups he discovered and explored is known as Mostow rigidity. His work on rigidity played an essential role in the work of three Fields medalists, namely Grigori Margulis, William Thurston, and Grigori Perelman.

Biography

Mostow was born in Boston, Massachusetts. His parents were Jews from Ukraine who immigrated to the United States in the early 20th century. Mostow attended the Boston Latin School and Hebrew College before going to Harvard University, where he received his bachelor's degree in mathematics in 1943 and followed by his Ph.D. in mathematics in 1948. His Ph.D. thesis was written under the supervision of Garrett Birkhoff. His academic appointments had been at Syracuse University from 1949 to 1952, at Johns Hopkins University from 1952 to 1961, and at Yale University from 1961 until his retirement in 1999. He died on April 4, 2017.

Honors

Mostow was elected to the National Academy of Sciences in 1974, served as the President of the American Mathematical Society in 1987 and 1988, and was a Trustee of the Institute for Advanced Study in Princeton, New Jersey from 1982 to 1992. He was awarded the AMS Leroy P. Steele Prize for Seminal Contribution to Research in 1993 for his book Strong rigidity of locally symmetric spaces (1973). In 1993 he was awarded the American Mathematical Society's Leroy P. Steele Prize for Seminal Contribution to Research. In 2013, he was awarded the Wolf Prize in Mathematics "for his fundamental and pioneering contribution to geometry and Lie group theory."