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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