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Awards | Fields Medal - 2014

Mathematics Sergey Lando and Alexander Bufetov the importance Award Maryam

Mirzakhani, its contribution to modern science and "random geometry"

14.8.2014

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In 2014, the first time in the 78 year history of the Fields Medal was awarded to a woman. Winner of theaward for outstanding contribution to the dynamics and geometry of Riemann surfaces was themathematician of Iran Maryam Mirzakhani. PostNauka asked mathematicians Sergey Lando andAlexander Bufetova comment on this important event and to talk about the subject of study of the winner

Sergey Lando

Doctor of Physical and Mathematical Sciences, Dean of the Faculty of Mathematics, School of Economics

The award of the Fields Medal of the International Mathematical Union for 2014 Maryam Mirzakhani - expected, but they are not less significant event.It seems that for the past few cycles Fields medal committee sought the opportunity to award the first woman to medal, and Mirzakhanov his remarkablework done by the same young age, he has provided such an opportunity. I think that in the next 4 years of the award of the Fields Medal women stopsurprising. Speaking at a meeting of the Moscow Mathematical Society, dedicated to the results of the previous International Congress of Mathematicians 2010, I have devoted a significant part of his speech, namely the report Maryam Mirzakhani. I knew her work prior to the invitation to

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the congress, but its report made a strong impression with freshness and a holistic view of the study area and the sequence in setting and achieving goalsAt present the Seoul Congress, she was invited as already the most honorable, the plenary speaker.

Viewpoint | Sexism in science

Expert Opinions PostNauki problem of gender discrimination in the academic environment

Works devoted to the structure of space Mirzakhanov possible geometries on two-dimensional surfaces.In this respect they resemble the work of Perelman - once he learns more complex case of three-dimensional surfaces. At the expense of smaller dimension in the two-dimensional case it is possible to obtain more complete results. Works Mirzakhanov use very deep and subtle geometric designsassociated with the possible values of the lengths of closed geodesics on a separate surface. In turn, the results allow us to compute the importantcharacteristics of the spaces of geometry, and much of it brought to the explicit computation of answers - a rare and highly valued because the quality of the scientific community.

In recent years Mirzakhanov develops original nonclassical probabilistic approaches to classic questions. As a consequence, many of the results areformulated as properties of "random geometry." There is reason to believe that the geometry of our space as in some sense accidental and that thereby thlanguage of chance may be adequate language to describe it.

Maryam Mirzakhani got school and university education in Iran, known for its high traditions of teaching mathematics. In school, she twice won goldmedals in the International Mathematical Olympiad. She wrote a doctoral thesis at Harvard University, USA, under the guidance of the winner CurtisFields Makmullena, and her work will certainly bear the stamp of close interaction with him.

Alexander Bufetov

Doctor of Physics and Mathematics, Professor HSE

Award Fields remarkable Iranian Maryam Mirzakhani mathematics - the solution is naturally expected and delivered us, her colleagues, great joy.

This prize was awarded to Miriam for a wide range of works, but I would like to talk about the work on ergodic theory in the Teichmüller space.Teichmüller space - a wonderful property! It parameterizes all the geometry, perhaps on a two-dimensional surface. Two-dimensional surface iscompletely classified in the XIX century. One can imagine the surface of a soccer ball (sphere) or donut (torus), but much more interesting to consider the bagel, which is usually called the "pigtail", as mathematicians call it "pretzel". Pretzel is a two donut connected tube. The geometry of the pretzel is

much richer than the geometry of the torus or a sphere. This is due to the fact that the geometry of the torus, for example, a Euclidean. But in studyingthe geometry of Lobachevsky pretzel occurs (this connection is opened and examined by Henri Poincaré). The set of all possible geometries on a pretzeland gives the Teichmüller space.

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FAQ: The axiomatic method

6 facts about the problem of mathematical proofs of Hilbert's program and the sense in mathematics

In the Teichmüller space is the so-called "geodetic" lines running along the shortest distance. Such lines have unusual chaotic properties. They satisfy thecentral limit theorem of probability theory. They are similar to the trajectory of Brownian motion. However, the situation changes completely if weconsider the complex geodesic - unlike real geodesic, they have the property of hardness. Maryam Mirzakhani in his joint work with Alexander Grigoryevich Eskin gave a full description of complex geodesics in Teichmüller space. Mirzakhanov belongs to large series of works, joint with Eskin.Some attended and other mathematicians, among them, and I: with Atreus and Eskin, we calculate the asymptotic volume of the ball in the Teichmüller space. Duke Math. J. Volume 161, Number 6 (2012), 1055-1111. Lattice point asymptotics and volume growth on Teichmüller space.Jayadev Athreya, Alexander Bufetov, Alex Eskin, and Maryam Mirzakhani.

Question descriptions of complex geodesics in Teichmüller space was a long time ago, worked on it a lot of mathematics. The problem itself dates back to the famed result 1991, resulting pupil Yakov Sinai Marina Ratner. Speaking very informally, Ratner fully describe the orbit of a wide class of dynamical systems arising in the theory of numbers. Pretty soon there was a question of transferring Ratner's theorem on the Teichmüller space. Eskinand Mirzakhanov gave a complete solution to this problem. It was a very long and difficult path, based, of course, at work and other mathematicians,among other approaches to Eskin and Mirzakhanov important role played by the wonderful work of the French mathematician Benoit and Kent.Breakthrough rarely appears by itself, it often relies on the research of many predecessors. Job Eskin and Mirzakhanov - wonderful breakthrough thatopens, in turn, the way to new research.

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• •

Радик Муртазин  • 

Как же это стрёмно видеть учёного-мусульманина :(

• •

Natalia Ivankina  • 

Радик, а где же сказано, что она мусульманка ?

• •

Алена  • 

Имя у нее арабское, скорее всего арабка, а значит мусульманка

• •

Angren  • редакция

С чего вы взяли, что она мусульманка? Если она из Ирана - это не гарантирует ее религиозную принадлежность. А судя по

обилию ее фотографий без платка/никаба/хиджаба напрашивается вывод, что она скорее не религиозна.

•   •

Радик Муртазин  • 

Но почему-то постнаука выбрала для твита именно мусульманскую фотку.

• •

Женя  • 

Ну вы ведь теперь понимаете, что у вас не совсем правильный образ Ирана в голове сложился?)

• •

Радик Муртазин  • 

К сожалению ораз Ирана определяют не учёные, а мусульмане.

• •

Igor Shtik  • 

 А вы почитайте про Ст ива Джобса и всё поймёте.

• •

Радик Муртазин  • Да почти всё прочитал. Что конкретно вы имеете ввиду?

• •

Igor Shtik  • 

То, что он пальцем деланный, а его биологический отец 'араб', а среди арабов, как мы знаем, подавляющее

большинство мусульман.

• •

Радик Муртазин  • 

Джобс-то тут причём? Он то не мусульманин.

• •

sed non satiata  • 

Как же это стрёмно видеть человека, пьющего водку :(

• •

sed non satiata  • 

Ведь все русские пьют водку, так ведь?

• •

Радик Муртазин  • 

Очень стрёмно, Но именно они и определяют обрас России, а не Перельман или Ландау.

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 Дисплазия соединительной ткани

•

  — - дисплазию ткани связали с высоким уровнем IQ - вот чего

уж нельзя подумать глядя на …

Разработка операционной системы рыночного уровня …

•

  — Этот ихний несуществующий «фантом»

уже много лет как притча во языцех. …

Запрещенные химические соединения

•

 — До некоторой степени "сложные" - да, но жизнь там

представить очень …

Исследования микробных сообществ в России

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 — - я столько пересмотрел лекций на постнаука что скоро са

буду микробиологом. Лекции …

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