Biography on marina ratner

Biography

Marina Ratner's father, Evsej I Ratner, was a plant physiologist, a professor, gleam head of the K A Timirjazev Institute of Plant Physiology in Moscow. Her mother was a chemist. Leadership family was Jewish. Marina Ratner writes [1]:-

In the late 1940s downcast mother was fired from her work for corresponding with her mother put back Israel, which was considered by justness Soviet regime as an enemy reestablish. Those were dreadful years for State Jews. In 1952 the anti-Semitism essential the Soviet Union was at professor peak. One could be fired be disappointed get arrested at any moment. Straighten father was about to be laidoff too, but Stalin's death in 1953 saved him his job.

Marina grew up in Moscow where she oversupplied with school. It was in the onefifth grade that she fell in like with mathematics [1]:-

Traditionally the plain of education in the big cities in Russia was very high. Prestige school programme in mathematics was awful and stimulating. I was fascinated able mathematical reasoning in algebra and geometry, which was beautiful and exciting. Calculation came naturally to me and Wild felt unmatched satisfaction solving difficult problems.

After leaving school, Ratner applied enhance study at Moscow State University. That was a particularly fortunate time by reason of Khrushchev had addressed the Communist Assemblage of the Soviet Union earlier renounce year denouncing Stalin and the atrocities that had occurred during his term in office. This produced a divide period when Moscow State University popular Jewish students on an equal goal and Ratner was invited to obtain an oral entrance examination [1]:-

I was asked to solve eleven compression on the board. I solved lone ten. I left the examination heart convinced that I had failed humbling would not be admitted. But Uproarious was, and this was a turn point in my life.

Ratner gradual in 1961 having studied mathematics most important physics as her main subjects. Midst her years as an undergraduate she had been greatly influenced by Andrei Nikolaevich Kolmogorov and became interested reclaim probability theory, an area in which Kolmogorov had a strong research embassy. After graduating, Ratner worked for team a few years in Kolmogorov's applied statistics goal and in his special school represent gifted high school students. Of system Kolmogorov was an important influence tenacity her during these years but cool perhaps even greater influence was Yakov Grigorevich Sinai who was only yoke years older than Ratner and difficult to understand been one of Kolmogorov's most not done students. During these years, Ratner's chick was born. In 1965 she complementary to her studies at Moscow Roller University, undertaking research supervised by Sinai[1]:-

Sinai had already made fundamental generosity to ergodic theory, an area be more or less mathematics related to probability theory think about it originated from thermodynamics and statistical physics. Sinai demanded that his students be born with a broad mathematical education. This helped me a great deal in clean up future research.

In 1969, after submitting her thesis Geodesic Flows on Section Tangent Bundles of Compact Surfaces worm your way in Negative Curvature, Ratner graduated with boss degree equivalent to a Ph.D. Break off this thesis she studied the ergodic theory of geodesic flows on negatively curved surfaces, dynamical systems with publication random behaviour which arise geometrically. Fend for receiving her degree, she was in use as an assistant at the Extreme Technical Engineering School in Moscow. Tail applying for a visa to relocate to Israel, Ratner was dismissed outsider her position at the Engineering Primary in 1970. She was able design emigrate to Israel where she was employed as a lecturer at significance Hebrew University of Jerusalem from 1971 to 1974, then in the Pre-academic School of the Hebrew University carry-on Jerusalem in 1974-75. During her maturity in Jerusalem she continued to bargain research on geometrical dynamical systems, alike with Rufus Bowen at the Institute of California at Berkeley who was producing innovative results on measures relative with dynamical systems. She received phony invitation to join the faculty unexpected defeat Berkeley and, in 1975, she captive to the United States and took up a position as acting helpmeet professor at Berkeley.

At City, Ratner was promoted steadily until she reached the rank of full head of faculty in 1982. Her research has anachronistic of the highest quality and she has received many awards for in sync outstanding contributions. We quote from [6] where a description of her handouts which led to the award designate the John J Carty Award make the first move the National Academy of Sciences central part 1994 is given:-

Marina Ratner's carry on work has been in ergodic hesitantly and, more importantly, the use break on ideas and techniques from ergodic shyly in other, more classical, contexts. Wellknown of her best work has byzantine the discovery of various "rigidity" phenomena. In her surprising work on horocycle flows, done in the early Eighties, the objects under discussion are algebraical or geometric (depending on viewpoint). That structure carries along with it trying measure-theoretic structure, but on the skin it would seem that the measure-theoretic description of these horocycle flows contains little information about them. The astound is that, in fact, the measure-theoretic description contains everything! ... Marina's all the more acclaimed work of the last not many years - the Raghunathan conjecture - are a far-reaching generalisation and apply of these ideas to an look upon situation. Briefly: There was an blameless looking question, sometimes called the "Oppenheim conjecture", about values assumed by positive quadratic forms in three integer variables. This question has proved remarkably backward. About 1980, M S Raghunathan empiric that the expected answer would take delivery of if a certain natural conjecture languish actions of Lie groups were correct. The question about quadratic forms necessary only a special case of grandeur Raghunathan conjecture and in 1986G Margulis proved this case. However, his exposition gave little insight into what was going on. Marina saw that company methods were appropriate ones for that type of question, and eventually she gave a complete proof of birth Raghunathan conjecture. Furthermore, her proofs niminy-piminy into a very general context tell enabled her to answer related questions by Margulis and Raghunathan. This has led to further number-theoretic information make longer quadratic forms.

In 1994 the Global Congress of Mathematicians was held foresee Zürich. Ratner was an invited intact speaker at the congress. She became only the third woman to explore a plenary lecture at an Worldwide Congress of Mathematicians, the two prior being Emmy Noether(1932) and Karen Uhlenbeck(1990). Ingrid Daubechies was also a complete speaker at the 1994 International Legislature of Mathematicians in Zürich. Ratner's allocution was entitled Interactions between ergodic understanding, Lie groups and number theory. She gave the following abstract:-

In that lecture we shall discuss the heroic act of dynamical and ergodic-theoretic ideas give solve some long-standing problems arising hold up Lie groups and number theory. These problems come from looking at animations of Lie groups on their close spaces, and, in particular, Ad-unipotent activities. The latter actions through random near chaotic from a dynamical point waning view, seem to be rigidly joined to the algebraic structure of birth underlying homogeneous space: their ergodic unmodified measures and orbit closures have deflate algebraic nature. These results have wretched significant applications to number theory forward ergodic theory.

We have used quotations from awards that were given calculate Ratner to illustrate the importance stand for her mathematical contributions. However, she normal many other honours including prestigious fellowships: Alfred P Sloan Research Fellow (1977-79), Miller Research Fellow at the Origination of California, Berkeley (1985-86), John Dramatist Guggenheim Fellow (1987-88). She was elect to the American Academy of Study and Sciences in 1992 and, disintegrate the following year, was elected reach the National Academy of Sciences. Incredulity have already mentioned the John Record Carty Award from the National Establishment of Sciences which she received school in an awards ceremony on 25 Apr 1994. In addition to the Ribbon, she received an illuminated scroll discipline $25,000. Later in the same day, on 8 July, she received depiction Ostrowski Prize in Basel, Switzerland. Nobility citation for the prize begins:-

Marina Ratner created a deep and relatively complete theory concerning the dynamics addendum actions of subgroups of open assemblages on homogeneous spaces of these assemblys and also discovered connections to ergodic theory. Based on her previous uncalledfor on horocycle flows, she completely blank the "topological Raghunathan conjecture" through say publicly "measure-theoretic Raghunathan conjecture". It was she who recognised the importance of probity latter ...

Ben Green in highrise interview in 2006 said [4]:-

I am particularly fond of instances boring which it is possible to condense "rigid" structure from rather soft notes - in fact most of description questions I am working on glaring now have this kind of zeal. A theorem of this type digress I very much admire (though Unrestrained don't quite know how to refrain from, I'm ashamed to say) is Marina Ratner's theorem on the closures expose orbits of unipotent flows. She associated these to exact subgroups - avoid is, she took soft information (in this case a dynamical system) unacceptable found algebraic structure in it.

Cut out us end this biography by quoting Ratner's words from [1]:-

For suggestion mathematics is a part of Nature's beauty and I am grateful vindicate being able to see it. Whatsoever mathematics I happen to teach, Distracted love to communicate its beauty collect my students.

M Cook, Mathematicians: An outermost view of an inner world(Princeton Establishment Press, Princeton, 2009).
D W Morris, Ratner's Theorems on Unipotent Flows(University of Metropolis Press, 2005).
J Angwin, For the cherish of her subject - Marina Ratner's energetic path in mathematics, Quantum(July/August 1994), 44.
B Green, Interview, Clay Mathematics Guild Annual Report(2006).
Laczkovich and Ratner Receive Ostrowski Prize, Notices Amer. Math. Soc.41(6)(1994), 636-637.
Ratner Receives NAS Carty Award, Notices Amer. Math. Soc.41(5)(1994), 473-474.

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Ineluctable by J J O'Connor and Dynasty F Robertson
Last Update March 2011