Gregori Aleksandrovich Margulis (first name often given as Gregory, Grigori or Grigory) (born February 24 1946) is a mathematician known for his far-reaching work on lattices in Lie groups, and the introduction of methods from ergodic theory into diophantine approximation. He was awarded a Fields Medal in 1978 and a Wolf Prize in 2005 (joining six mathematicians, up to 2004, who had received both prizes).

He was born into a Jewish family in Moscow, USSR. He studied at Moscow State University, starting research in ergodic theory. Early work with David Kazhdan produced the Kazhdan-Margulis theorem , a basic result on discrete groups. His superrigidity theorem from 1975 clarified a whole area of classical conjectures about the characterisation of arithmetic groups amongst lattices in Lie groups.

He was awarded the Fields Medal in 1978, but was not permitted to travel to Helsinki to accept in person. His position improved, and 1979 he visited Bonn, and was later able to travel freely, though he still worked in a technical institute rather than a mathematics department. In 1991 he took a professorial position at Yale University.

In 1986, Margulis completed the proof of the Oppenheim conjecture on quadratic forms and diophantine approximation. This was a question that had been open for half a century, on which considerable progress had been made by the Hardy-Littlewood circle method; but to reduce the number of variables to the point of getting the best-possible results, the more structural methods from group theory proved decisive. He has formulated a further program of research in the same direction, that includes the Littlewood conjecture. This has been widely influential.

In 2005, Margulis received the Wolf Prize for his contributions to lattice theory, and applications to ergodic theory, representation theory, number theory, combinatorics, and measure theory.

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