Marina Evseevna Ratner (russian: Мари́на Евсе́евна Ра́тнер; October 30, 1938 – July 7, 2017) was a professor of mathematics at the
University of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...
who worked in
ergodic theory
Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...
. Around 1990, she proved a group of major theorems concerning
unipotent
In mathematics, a unipotent element ''r'' of a ring ''R'' is one such that ''r'' − 1 is a nilpotent element; in other words, (''r'' − 1)''n'' is zero for some ''n''.
In particular, a square matrix ''M'' is a unipotent ...
flows on
homogeneous space
In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group ''G'' is a non-empty manifold or topological space ''X'' on which ''G'' acts transitively. The elements of ' ...
s, known as
Ratner's theorems
In mathematics, Ratner's theorems are a group of major theorems in ergodic theory concerning unipotent flows on homogeneous spaces proved by Marina Ratner around 1990. The theorems grew out of Ratner's earlier work on horocycle flows. The study ...
. Ratner was elected to the
American Academy of Arts and Sciences
The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...
in 1992, awarded the
Ostrowski Prize
The Ostrowski Prize is a mathematics award given every odd year for outstanding mathematical achievement judged by an international jury from the universities of Basel, Jerusalem, Waterloo and the academies of Denmark and the Netherlands. Alexand ...
in 1993 and elected to the
National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...
the same year. In 1994, she was awarded the
John J. Carty Award from the National Academy of Sciences.
Biographical information
Ratner was born in
Moscow
Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...
,
Russian SFSR
The Russian Soviet Federative Socialist Republic, Russian SFSR or RSFSR ( rus, Российская Советская Федеративная Социалистическая Республика, Rossíyskaya Sovétskaya Federatívnaya Soci ...
to a Jewish family, where her father was a plant physiologist and her mother a chemist. Ratner's mother was fired from work in the 1940s for writing to her mother in Israel, then considered an enemy of the Soviet state. Ratner gained an interest in mathematics in her fifth grade. From 1956 to 1961, she studied mathematics and physics at
Moscow State University
M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...
. Here, she became interested in
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
, inspired by
A.N. Kolmogorov and his group.
After graduation, she spent four years working in Kolmogorov's applied statistics group. Following this, she returned to Moscow State university for graduate studies were under
Yakov G. Sinai
Yakov Grigorevich Sinai (russian: link=no, Я́ков Григо́рьевич Сина́й; born September 21, 1935) is a Russian-American mathematician known for his work on dynamical systems. He contributed to the modern metric theory of dy ...
, also a student of Kolmogorov. She completed her PhD thesis, titled "Geodesic Flows on Unit Tangent Bundles of Compact Surfaces of Negative Curvature", in 1969. In 1971 she emigrated from the Soviet Union to Israel and she taught at the
Hebrew University
The Hebrew University of Jerusalem (HUJI; he, הַאוּנִיבֶרְסִיטָה הַעִבְרִית בִּירוּשָׁלַיִם) is a public research university based in Jerusalem, Israel. Co-founded by Albert Einstein and Dr. Chaim Weiz ...
from 1971 until 1975. She began to work with
Rufus Bowen
Robert Edward "Rufus" Bowen (23 February 1947 – 30 July 1978) was an internationally known professor in the Department of Mathematics at the University of California, Berkeley, who specialized in dynamical systems theory. Bowen's work dealt pr ...
at Berkeley and later emigrated to the United States and became a professor of mathematics at Berkeley. Her work included proofs of conjectures dealing with unipotent flows on quotients of Lie groups made by
S. G. Dani
Shrikrishna Gopalrao Dani is a professor of mathematics at the Centre for Excellence in Basic Sciences, Mumbai who works in the broad area of ergodic theory.
Education
He did a master's degree from the University of Mumbai in 1969. He then joi ...
and
M. S. Raghunathan
Madabusi Santanam Raghunathan FRS is an Indian mathematician. He is currently Head of the National Centre for Mathematics, Indian Institute of Technology, Mumbai. Formerly Professor of eminence at TIFR in Homi Bhabha Chair. Raghunathan receiv ...
. For this and other work, she won the
John J. Carty Award for the Advancement of Science
The John J. Carty Award for the Advancement of Science is awarded by the U.S. National Academy of Sciences "for noteworthy and distinguished accomplishments in any field of science within the charter of the Academy". Established by the America ...
in 1994. she became only the third woman plenary speaker at International Congress of Mathematicians in 1994.
Marina Ratner died July 7, 2017, at the age of 78.
Selected publications
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References
{{DEFAULTSORT:Ratner, Marina
1938 births
2017 deaths
American women mathematicians
Fellows of the American Academy of Arts and Sciences
Members of the United States National Academy of Sciences
20th-century American mathematicians
21st-century American mathematicians
Jewish Russian scientists
Jewish American scientists
University of California, Berkeley faculty
Dynamical systems theorists
20th-century women mathematicians
21st-century women mathematicians
Russian women scientists
20th-century Russian mathematicians
20th-century American women
21st-century American women
20th-century Russian women
21st-century American Jews