Mikhael Gromov (mathematician) facts for kids

Quick facts for kids Mikhael Gromov
Михаил Громов
Gromov in 2014
Born	(1943-12-23) 23 December 1943 (age 81) Boksitogorsk, Russian SFSR, Soviet Union
Nationality	Russian and French
Alma mater	Leningrad State University (PhD)
Known for	Geometric group theory Symplectic geometry Systolic geometry Gromov boundary Gromov's compactness theorem (geometry) Gromov's compactness theorem (topology) Gromov's theorem on groups of polynomial growth Gromov–Hausdorff convergence Gromov–Ruh theorem Gromov–Witten invariant Gromov hyperbolic group Gromov δ-hyperbolic space Gromov norm Gromov product Gromov topology Gromov's inequality for complex projective space Gromov's systolic inequality Bishop–Gromov inequality Asymptotic dimension Essential manifold Filling area conjecture Filling radius Mean dimension Minimal volume Non-squeezing theorem Pseudoholomorphic curve Random group Sofic group Systolic freedom 2π theorem
Awards	Oswald Veblen Prize in Geometry (1981) Wolf Prize (1993) Balzan Prize (1999) Kyoto Prize (2002) Nemmers Prize in Mathematics (2004) Bolyai Prize (2005) Abel Prize (2009)
Scientific career
Fields	Mathematics
Institutions	Institut des Hautes Études Scientifiques New York University
Doctoral advisor	Vladimir Rokhlin
Doctoral students	Denis Auroux François Labourie Pierre Pansu Mikhail Katz

Mikhael Leonidovich Gromov (born 23 December 1943) is a famous Russian-French mathematician. He is known for his important work in geometry, analysis, and group theory. He works at the Institut des Hautes Études Scientifiques in France and is a professor at New York University.

Gromov has won many awards, including the Abel Prize in 2009. This prize was given to him "for his revolutionary contributions to geometry."

Early Life and Education

Mikhael Gromov was born on December 23, 1943, in Boksitogorsk, which was part of the Soviet Union at the time. His parents were both pathologists, which means they studied diseases. His mother was also a cousin of the famous chess champion Mikhail Botvinnik.

Mikhael was born during World War II. His mother, who was a doctor in the Soviet Army, had to leave the war front to give birth to him. When he was nine years old, his mother gave him a book called The Enjoyment of Mathematics. This book made him very curious about math and had a big impact on his future.

Gromov studied mathematics at Leningrad State University. He earned his master's degree in 1965 and his doctorate in 1969. He completed his postdoctoral thesis in 1973. His main teacher and advisor was Vladimir Rokhlin.

Moving to a New Country

Gromov got married in 1967. In 1970, he was invited to speak at a big math conference in Nice, France. However, the Soviet Union did not allow him to leave the country. Even so, his speech was still printed in the conference's official papers.

From a young age, Gromov wanted to leave the Soviet system. In the early 1970s, he stopped publishing his math papers. He hoped this would help him get permission to move to Israel. He even changed his last name to his mother's name.

Finally, in 1974, his request to leave was approved. He moved to New York and started working at Stony Brook University.

Life and Work in France and the US

In 1981, Mikhael Gromov left Stony Brook University. He joined the faculty at the University of Paris VI in France. In 1982, he became a permanent professor at the Institut des Hautes Études Scientifiques, where he still works today.

At the same time, he also taught at the University of Maryland, College Park from 1991 to 1996. Since 1996, he has been a professor at the Courant Institute of Mathematical Sciences in New York. In 1992, he became a French citizen.

Gromov's way of looking at geometry is often described as "coarse" or "soft." This means he focuses on the big picture and long-term properties of shapes and spaces, rather than tiny details. He is also interested in mathematical biology, how the brain works, and how scientific ideas develop.

Key Contributions to Mathematics

Mikhael Gromov has made many important discoveries in different areas of mathematics.

Understanding Shapes and Spaces

Gromov introduced the idea of the h-principle. This principle helps mathematicians understand when certain complex geometric problems can be solved. For example, he showed that you can create shapes with positive or negative curves on any "open manifold" (a type of space). This was a big discovery because it went against some older ideas about how shapes could be curved.

He also wrote a well-known book called Partial Differential Relations. This book brings together much of his work on these kinds of problems. Later, he used his methods to study complex geometry, which deals with shapes using complex numbers.

Measuring Distances and Groups

In 1981, Gromov created the Gromov–Hausdorff metric. This is a special way to measure the "distance" between different metric spaces (spaces where you can measure distances between points). This tool helps mathematicians compare very different kinds of shapes and spaces.

He also developed an important "compactness theorem." This theorem gives conditions under which a sequence of spaces will "converge" or get closer to a limit space. This idea has been very important in a field called geometric group theory.

Gromov used these ideas to study the "asymptotic geometry" of groups. He showed that certain groups, when looked at on a very large scale, have unexpected smooth properties. This helped him solve the Milnor-Wolf conjecture, which states that groups with "polynomial growth" are "virtually nilpotent" (a specific type of group).

Along with Eliyahu Rips, Gromov also came up with the idea of hyperbolic groups. These are groups that behave in a way similar to hyperbolic geometry, which is a type of geometry where parallel lines can diverge.

Symplectic Geometry Discoveries

Gromov's work on pseudoholomorphic curves is a key part of modern symplectic geometry. This area of math studies spaces that have a special way of measuring area and volume. He discovered a "bubbling" effect in these curves, similar to what happens in other areas of geometry.

One of his most famous results is the "non-squeezing theorem." This theorem shows a surprising feature of symplectic geometry: you cannot squeeze a round ball into a much thinner cylinder if you only use certain types of transformations. This was a very important discovery that showed how different symplectic geometry is from regular geometry.

Gromov's ideas also helped create Gromov-Witten theory. This theory is studied in many fields, including string theory and algebraic geometry.

Awards and Recognition

Mikhael Gromov has received many prestigious awards and honors for his groundbreaking work in mathematics.

Major Prizes

• Prize of the Mathematical Society of Moscow (1971)
• Oswald Veblen Prize in Geometry (1981)
• Prix Elie Cartan (1984)
• Prix de l'Union des Assurances de Paris (1989)
• Wolf Prize in Mathematics (1993)
• Leroy P. Steele Prize (1997)
• Lobachevsky Medal (1997)
• Balzan Prize for Mathematics (1999)
• Kyoto Prize in Mathematical Sciences (2002)
• Nemmers Prize in Mathematics (2004)
• Bolyai Prize (2005)
• Abel Prize (2009)

Honors and Memberships

Gromov has been invited to speak at many important math conferences around the world. He is also a member of several highly respected scientific academies, including:

• The National Academy of Sciences (USA)
• The American Academy of Arts and Sciences
• The Norwegian Academy of Science and Letters
• The Royal Society (UK)
• The National Academy of Sciences of Ukraine
• The French Academy of Sciences

See also