Grigory Alexandrovich Margulis

Grigori Margulis

Grigori Alexandrowitsch Margulis (also Gregori or Grigori ; born February 24, 1946 in Moscow ) is a Russian mathematician who received the Fields Medal in 1978 and the Abel Prize in 2020 for his work on group theory , combinatorics , measure theory , ergodic theory and number theory .

Life

He was born into a Jewish family in Moscow and studied at the local university under Jakow Grigorjewitsch Sinai , where he initially worked on ergodic theory . He received his PhD in 1970 (candidate title) and then worked at the Information Transmission Institute, where he stayed through the 1970s and 1980s and became senior scientist in 1986. In 1991 he became a professor of mathematics at Yale University .

His PhD students include Hee Oh and Emmanuel Breuillard .

plant

With David Kazhdan he proved the Kazhdan-Margulis theorem about discrete groups . In 1975 he proved the superstiffness theorem for lattices in symmetric spaces of rank . This intensifies Mostow's rigidity theorem and states that representations of these lattices either have a finite image or can be continued to represent the surrounding Lie group. As a corollary to the superstiffness theorem, he proved that lattices in symmetric spaces of rank must always be arithmetic groups . ${\displaystyle \geq 2}$ ${\displaystyle \geq 2}$

In 1986 he proved the Oppenheim conjecture (from 1929) about quadratic forms and Diophantine approximations . It says that an indefinite quadratic form in variables ( ) that is not a real multiple of a form with rational coefficients takes on values ​​as a function of the integers that are close to the real numbers. ${\displaystyle n}$ ${\displaystyle n\geq 3}$

Honors and memberships

In 1978 he received the Fields Medal , but was not allowed to receive it in Helsinki . He was only able to travel abroad (to Bonn ) in 1979 .

In 2005 he received the Wolf Prize . In 1990 he gave a plenary lecture at the ICM in Kyōto (Dynamical and ergodic properties of subgroup actions of homogeneous spaces with applications to number theory).

In 1968 he received the Moscow Mathematical Society Prize .

In 1991 he received the medal of the College de France and in 1995 the Humboldt Research Prize . In addition, he received the Lobachevsky Prize of the Russian Academy of Sciences in 1996. He is a member of the Tata Institute of Fundamental Research (1996), the American Academy of Arts and Sciences (1992) and the National Academy of Sciences . He is a fellow of the American Mathematical Society .

In 2020 he received the Abel Prize with Hillel Fürstenberg .

See also

• Lemma of Margulis
• Margulis' super rigidity theorem

Web links

• John J. O'Connor, Edmund F. Robertson :  Grigori Alexandrowitsch Margulis. In: MacTutor History of Mathematics archive .
• Entry on Grigori Alexandrowitsch Margulis at Math-Net.Ru
• Jacques Tits: Travaux de Margulis sur les sous-groupes discrets de groupes de Lie. Séminaire Bourbaki, 18 (1975-1976), French.
• L. Ji: A summary of the work of Margulis (PDF; 428 kB)
• Videos by and about Grigori Alexandrowitsch Margulis in the AV portal of the Technical Information Library

swell

1. ↑ Grigori Alexandrowitsch Margulis in the Mathematics Genealogy Project (English)
2. ↑ Climate as in Kafka SPIEGEL 3/1979
3. ^ Lobachevsky Medal - Prize Winner