Yale’s Gregory A. Margulis, widely considered one of the most innovative and influential mathematicians of the past half-century, has been awarded the Abel Prize in Mathematics — among the world’s leading honors in mathematics, along with the Field Medal and the Wolf Prize.
Margulis, the Erastus L. DeForest Emeritus Professor of Mathematics, has now won all three honors: He won the Wolf Prize in 2005 and the Fields Medal in 1978.
The King of Norway will present the Abel Prize to Margulis and co-winner Hillel Furstenberg of the Hebrew University of Jerusalem. A ceremony previously scheduled for May will be rescheduled due to concerns relating to coronavirus-2019.
“Just browsing a survey of his major accomplishments gives one an almost surreal experience of wondering how one mathematician could have produced such a wide range of results, each of which was so deep and many of which had been considered inaccessible,” said Hee Oh, Yale’s Abraham Robinson Professor of Mathematics and a former Margulis Ph.D. student.
“His solutions are stunning because of their beauty and also because of such an exquisite use of a variety of seemingly unrelated mathematics. He is one of the most original mathematicians I have encountered in my mathematical career,” Oh said.
Margulis, 74, was born in Moscow and earned his Ph.D. in 1970 from Moscow State University. In 1978, when he won the Fields Medal, he was not allowed to leave the Soviet Union to accept the honor in Helsinki. In 1979, when Soviet academics were given more personal freedoms, Margulis was allowed to travel abroad. He visited academic institutions in Europe and the U.S. before joining the Yale faculty in 1991.
One of his greatest mathematical triumphs was his proof of the Selberg-Piatetskii-Shapiro Conjecture, which demonstrated that lattices — a type of abstract mathematical structure, akin to the symmetry patterns of periodic tilings — in higher-rank Lie groups are arithmetic in nature. As part of his work with lattices, Margulis introduced a major new tool for mathematicians, the Margulis Superrigidity Theorem.
Margulis solved the 1929 Oppenheim Conjecture, which concerns values of indefinite irrational quadratic forms at integer points; he gave the first explicit construction of expander graphs, which are highly useful for computer science; he also proved that quotients of lattices in higher-rank groups are always finite, which is called the Margulis normal subgroup theorem.
“Grisha’s work is fundamental in my own research, and his major results, of course, shape the entire field,” said Yair Minsky, the Einar Hille Professor and chair of mathematics at Yale. “He is an excellent colleague with a deep and detailed understanding of the way our profession works. There is an inexorable logic to his point of view that always brings me around. It has been both a pleasure and an honor to be his colleague.”
The Norwegian government established the Abel Prize in 2002 on the occasion of the 200th anniversary of the birth of Norwegian mathematician Niels Henrik Abel. The prize has been awarded annually by the Norwegian Academy of Science and Letters since 2003.
Margulis is the first Yale mathematician to receive the Abel Prize.
Margulis is a member of the National Academy of Sciences, a foreign honorary member of the American Academy of Arts and Sciences, an honorary fellow of the Tata Institute of Fundamental Research, and a fellow of the Fields Institute and the American Mathematical Society. He has also received the Medal of the College de France, a Humboldt Research Award, the Lobachevsky Prize, and the Dobrushin International Prize.
Margulis and Furstenberg will share a monetary award of 7.5 million NOK (approximately $834,000 in U.S. dollars).