Grigory Margulis

Erastus L.De Forest Professor of Mathematics

Grigory Margulis, B.A. and Ph.D. Moscow State University, faculty member at Yale since 1991: You have revolutionized the study of discrete subgroups of Lie groups, a field that combines geometry, symmetry, and dynamics, and has deep implications in many parts of mathematics and its applications.

You introduced new ideas and techniques from the very start of your career, taking the mathematical world by surprise. In 1978 you were awarded the prized Fields Medal for your Arithmeticity Theorem, and the celebrated Superrigidity Theorem on which it depended, but because of anti-Semitism you were not allowed to travel to Helsinki to accept the prize in person. Your position ultimately improved and you traveled quite widely, but not until you came to Yale in 1991 did you hold a university faculty position.

Your work combines ideas about symmetry, probability, and algebra, while the powerful and original techniques you have developed continue to guide the field, playing a recurring role in every significant new development. It is no accident that the “Margulis lemma” is a tool in every geometer’s toolkit, and that nearly every discussion in the field involves at some point the invocation of “Margulis’ thesis.”

Each of your advances solved an important and difficult problem, while introducing fresh ideas that reverberate throughout mathematics, opening entirely new subfields. Your famous solution of the Oppenheim conjecture, which is a statement about the values of irrational quadratic forms, showed the reach of techniques from ergodic theory and dynamics into the realm of algebra. You also showed how to use the theory of lattices to construct expander graphs, which are networks with robust connectivity properties of great importance in combinatorics and computer science.

Your influence carries on through your many graduate students and the postdocs you have mentored, who have gone on to solve significant and central problems of their own, and to open new avenues of research. Among your many richly deserved awards was the Wolf Prize in 2005, which cites your “monumental contributions to algebra, in particular to the theory of lattices in semi-simple Lie groups, and striking applications of this to ergodic theory, representation theory, number theory, combinatorics and measure theory.”

As chair of the department, and involved departmental citizen, you applied your uncompromising precision, deep knowledge of the profession, and your strong will to the betterment of your colleagues. Your wry sense of humor often serves to underline a serious point and cut through to the core of a debate. In the great tradition of the Department of Mathematics, where retired mathematicians continue to be active in the mathematical community, we look forward to many more years of interaction with you and with your ideas.