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Grigory Margulis
Grigory Margulis (2006).jpg
Margulis on his 60th birthday, 2006
Born (1946-02-24) February 24, 1946 (age 79)
Nationality Russian, American
Education Moscow State University (BS, MS, PhD)
Known for Diophantine approximation
Lie groups
Superrigidity theorem
Arithmeticity theorem
Expander graphs
Oppenheim conjecture
Awards Fields Medal (1978)
Lobachevsky Prize (1996)
Wolf Prize (2005)
Abel Prize (2020)
Scientific career
Fields Mathematics
Institutions Yale University
Thesis On some aspects of the theory of Anosov flows (1970)
Doctoral advisor Yakov Sinai
Doctoral students Emmanuel Breuillard
Hee Oh

Grigory Aleksandrovich Margulis (Russian: Григо́рий Алекса́ндрович Маргу́лис, born February 24, 1946) is a famous Russian-American mathematician. He is known for his important work on special mathematical structures called lattices and Lie groups. He also found new ways to use ideas from ergodic theory to solve problems in diophantine approximation.

Margulis has received many top awards in mathematics. He was given the Fields Medal in 1978, the Wolf Prize in Mathematics in 2005, and the Abel Prize in 2020. He is one of only a few mathematicians to win all three of these major prizes. Since 1991, he has been a professor at Yale University.

Early Life and Education

Grigory Margulis was born in Moscow, which was then part of the Soviet Union. His family was of Lithuanian Jewish descent. From a young age, he showed great talent in mathematics.

Math Olympiad Success

When he was just 16 years old in 1962, Margulis won a silver medal. This was at the International Mathematical Olympiad, a big competition for young math students from around the world.

University Studies

He went on to study at Moscow State University. In 1970, he earned his PhD. His research focused on a field called ergodic theory, which looks at how systems change over time. His advisor was the well-known mathematician Yakov Sinai.

Career and Achievements

Margulis's early work helped create important ideas in mathematics. He worked with another mathematician, David Kazhdan, on a key result about discrete groups. This is known as the Kazhdan–Margulis theorem.

Superrigidity Theorem

In 1975, Margulis developed his "superrigidity theorem." This theorem helped explain how certain mathematical groups are structured. It was a big step forward in understanding arithmetic groups within Lie groups.

International Recognition

Margulis was awarded the Fields Medal in 1978. This is often called the "Nobel Prize of mathematics." However, he was not allowed to travel from the Soviet Union to accept the award in person. Later, his situation improved, and he was able to travel more freely.

In 1991, Margulis moved to the United States. He accepted a position as a professor at Yale University.

Major Awards and Honors

Margulis has been recognized for his contributions to mathematics many times:

Key Mathematical Ideas

Margulis's work has had a huge impact on modern mathematics. He solved long-standing problems and opened up new areas of research.

Understanding Lattices

Much of his early work focused on understanding "lattices" in certain types of mathematical groups. He proved that many of these lattices, which are defined by their properties, are actually "arithmetic." This means they can be built in a specific, simpler way, similar to how you might think of matrices with only whole numbers. This discovery helped mathematicians classify these complex structures.

Solving the Oppenheim Conjecture

In 1986, Margulis completely solved the Oppenheim conjecture. This was a difficult problem about quadratic forms and diophantine approximation that had been unsolved for 50 years. His solution used new methods from group theory.

Expander Graphs

Margulis also created the first examples of what are called expander graphs. These are special types of networks that are very well-connected. They are important in computer science and other fields.

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