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A biography of Gregory Margulis

In a glittering mathematical career, Gregory arithmeticity and superrigidity theorems. (Grisha) Margulis has introduced many influential The arithmeticity theorem states that all irreducible ideas, solved long-standing open questions, and lattices in semi-simple Lie groups of rank greater discovered deep connections between different than 2 are arithmetic, and the superrigidity theorem mathematical fields. His signature approach has that a representation of such a lattice extends been to use in unexpected and to a representation of the ambient Lie . The ingenious ways, which has led to the creation of superrigidity proof demonstrated novel applications entirely new areas of study. of ergodic theory, establishing powerful new methods that became very influential in Born in in 1946, he gained international many fields. recognition aged 16 with a silver medal at the International Mathematical Olympiad. He attended ( laureate in 2008 ) said , receiving his PhD in of Margulis in 1978: “It is not exaggerated to say 1970 under the supervision of ( Abel that, on several occasions, he has bewildered the Prize laureate in 2014 ). His dissertation revealed experts by solving questions which appeared to be a particularly original mind: he constructed a completely out of reach at the time.” measure — now called the Bowen-Margulis measure — that enabled him to discover new Margulis, however, was unable to receive the Fields properties about the of hyperbolic space. Medal since the Soviet authorities refused him a His methods subsequently inspired many new visa to attend the awards ceremony in , questions and areas of active research. Finland. He was only allowed to travel abroad in 1979 when Soviet academics were given more Margulis won the 1978 , aged only 32, personal freedoms. During the 1980s, he visited for his work on lattices in Lie groups, notably his academic institutions in Switzerland, and the U.S., before settling at Yale in 1991, where he Kazhdan Property ( T ) from , has been ever since. on the other.

Earlier in his career, Margulis faced discrimination In 1984 he proved the Oppenheim conjecture, an for being of Jewish origin. Even though he was idea from first stated in 1929, using one of the top young in the methods from ergodic theory. More important than country, he was unable to find a job at Moscow the result was the whole idea of using ergodic University. Instead, he worked at the much less theory in this way, and this created a new area, now prestigious Institute for Problems in Information called homogenous dynamics. The work of three Transmission. His contact with colleagues at the recent Fields medallists — , institute, however, led to a remarkable discovery. and — all They told him about a type of connected network builds on Margulis’s earlier ideas. called an “expander graph”. Within days Margulis had constructed the first known example of an Margulis has been as prolific as he has been expander graph using ideas from representation diverse. When in 2008 the Pure and Applied theory, an abstract and seemingly unrelated . Mathematics Quarterly ran an article listing His discovery was ground-breaking and has had Margulis’s major results, it ran to more than many applications in computer science. 50 pages.

Margulis again demonstrated his knack for proving In 2001 Margulis was elected to the U.S. National theorems in stunning and surprising ways when Academy of Sciences. He is a winner of the in 1978 he revealed what is now called his normal and the Wolf Prize. theorem, about lattices in Lie groups. His proof was a very original combination of the Margulis and his wife Raisa (Raya) have a son and theory of amenable groups on one hand and the a granddaughter.