The Abel Prize Laureate 2014 Yakov G. Sinai Princeton University, USA, and Landau Institute for Theoretical Physics, Russian Academy of Sciences www.abelprize.no Yakov G. Sinai receives the Abel Prize for 2014 “for his fundamental contributions to dynamical systems, ergodic theory, and mathematical physics” for studying the complexity of a system dynamical systems as well as in the attempts Citation through a measure-theoretical description to tackle real-life complex chaotic behavior of its trajectories. It has led to very important such as turbulence. advances in the classification of dynamical Sinai’s other pioneering works in systems. mathematical physics include: random Sinai has been at the forefront of walks in a random environment (Sinai’s ergodic theory. He proved the first ergodicity walks), phase transitions (Pirogov–Sinai theorems for scattering billiards in the style theory), one-dimensional turbulence (the of Boltzmann, work he continued with statistical shock structure of the stochastic Bunimovich and Chernov. He constructed Burgers equation, by E–Khanin–Mazel– Markov partitions for systems defined by Sinai), the renormalization group theory iterations of Anosov diffeomorphisms, which (Bleher–Sinai), and the spectrum of discrete led to a series of outstanding works showing Schrödinger operators. the power of symbolic dynamics to describe Sinai has trained and influenced a various classes of mixing systems. generation of leading specialists in his The Norwegian Academy of Science and Some of these phenomena can be foreseen With Ruelle and Bowen, Sinai discovered research fields. Much of his research has Letters has decided to award the Abel Prize with great accuracy, while others seem to the notion of SRB measures: a rather general become a standard toolbox for mathematical for 2014 to evolve in a chaotic, unpredictable way. Now and distinguished invariant measure for physicists. His works had and continue it has become clear that order and chaos are dissipative systems with chaotic behavior. to have a broad and profound impact on Yakov G. Sinai intimately connected: we may find chaotic This versatile notion has been very useful mathematics and physics, as well as on the Princeton University, USA, and Landau behavior in deterministic systems, and in the qualitative study of some archetypal ever-fruitful interaction of these two fields. Institute for Theoretical Physics, Russian conversely, the statistical analysis of chaotic Academy of Sciences systems may lead to definite predictions. Yakov Sinai made fundamental “for his fundamental contributions to contributions in this broad domain, dynamical systems, ergodic theory, and discovering surprising connections between mathematical physics” order and chaos and developing the use of probability and measure theory in the study Ever since the time of Newton, of dynamical systems. His achievements differential equations have been used by include seminal works in ergodic theory, mathematicians, scientists and engineers to which studies the tendency of a system to explain natural phenomena and to predict explore all of its available states according how they evolve. Many equations incorporate to certain time statistics; and statistical stochastic terms to model unknown, mechanics, which explores the behavior of seemingly random, factors acting upon that systems composed of a very large number evolution. The range of modern applications of particles, such as molecules in a gas. of deterministic and stochastic evolution Sinai’s first remarkable contribution, equations encompasses such diverse inspired by Kolmogorov, was to develop an issues as planetary motion, ocean currents, invariant of dynamical systems. This invariant physiological cycles, population dynamics, has become known as the Kolmogorov–Sinai Photo: Princeton University, Department of Mathematics and electrical networks, to name just a few. entropy, and it has become a central notion 4 5 The deep contributions made by Sinai London Mathematical Society (1992), the Biography early in his career led to his being invited Hungarian Academy of Sciences (1993), the to lecture at the International Congress of United States National Academy of Sciences Mathematicians in Stockholm in 1962. Sinai (1999), the Brazilian Academy of Sciences has since been an invited speaker at several (2000), the Academia Europaea (2008), the important international conferences and has Polish Academy of Sciences (2009) and the given many prestigious lectures worldwide. Royal Society of London (2009). He has spoken four times at the International He has received honorary degrees Congress of Mathematicians. He was a from Warsaw University (1993), Budapest Yakov G. Sinai was born on 21 September During 1997-1998 Yakov Sinai was plenary speaker at the 1st Latin American University of Science and Technology (2002), 1935 in Moscow, Russia. Both of his parents, Thomas Jones Professor at Princeton Congress in Mathematics in 2000. In 2001 he the Hebrew University in Jerusalem (2005), Gregory Sinai and Nadezda Kagan, were University and in 2005 he was Moore was appointed Chairman of the Fields Medal and Warwick University (2010). microbiologists with research careers. His Distinguished Scholar at the California Institute Committee of International Mathematical Professor Sinai is also respected as a grandfather, the mathematician Benjamin of Technology in Pasadena, California. Union, which decided on the awards of the teacher at Princeton. In the words of a former Fedorovich Kagan, was head of the Yakov Sinai is one of the most influential Fields Medals at the Congress in Beijing in student, “It’s quite inspirational to be in his Department of Differential Geometry at mathematicians of the twentieth century. the following year. class … People feel an immediate urge to Moscow State University. Kagan had great He has achieved numerous groundbreaking participate – there is a radiance which comes influence on his grandson. He retired from results in the theory of dynamical systems, Awards and honours from him and inspires us.”2 He is also known his chair at Moscow State University in in mathematical physics and in probability Yakov Sinai has received many distinguished for his persistence in the face of obstacles, be 1952, the year in which his grandson Yakov theory. Many mathematical results are named international awards. In 2013 he was awarded they bureaucratic or theoretical, a trait which Grigorevich entered the Faculty of after him, including Kolmogorov–Sinai the Leroy P. Steele Prize for Lifetime Achieve- has served him well throughout the years. Mechanics and Mathematics. entropy, Sinai’s billiards, Sinai’s random walk, ment from the American Mathematical — Yakov Sinai received his B.S. (1957), his Sinai-Ruelle-Bowen measures, and Pirogov- Society. Other awards include the Wolf Prize Ph.D. (1960), and his doctorate (1963) from Sinai theory. Sinai is highly respected in in Mathematics (1997), the Nemmers Prize For his 70th birthday in 2005 a special issue Moscow State University. His advisor was both physics and mathematics communities in Mathematics (2002), the Henri Poincaré of the Moscow Mathematical Journal was the prominent Andrey Kolmogorov. Sinai was as the major architect of the most bridges Prize from the International Association dedicated to Sinai: “Yakov Sinai is one of a Scientific Researcher at the Laboratory connecting the world of deterministic of Mathematical Physics (2009) and the the greatest mathematicians of our time. of Probabilistic and Statistical Methods at (dynamical) systems with the world of Dobrushin International Prize from the Institute The list of international prizes awarded to Moscow State University from 1960 to 1971. probabilistic (stochastic) systems. Perhaps it of Information Transmission of the Russian him as a sign of recognition of his scientific In 1971 he became a Professor at Moscow is only to be expected that he is the author Academy of Sciences (2009). Among his contributions is extremely long, and the list State University and a Senior Researcher at of an article titled “Mathematicians and many recognitions are the Boltzmann Gold of his fundamental results is even longer. 1 the Landau Institute of Theoretical Physics, Physicists = Cats and Dogs?” Medal from the Commission on Statistical His permanent interest in mathematics and Russian Academy of Sciences. Since 1993 During the past half-century Yakov Sinai Physics of the International Union of Pure and his exceptional scientific enthusiasm inspire he has been a Professor of Mathematics has written more than 250 research papers Applied Physics (1986) and the Dirac Medal several generations of scientists all over the at Princeton University, USA, but has and a number of books. Sinai and his wife from the Abdus Salam International Centre for world. His mere presence at a seminar or at concurrently kept his position at the Landau Elena B. Vul, a mathematician and physicist, Theoretical Physics in Trieste (1992). a conference makes scientific life brighter Institute of Theoretical Physics. The Landau have also written a number of joint papers. Many mathematical societies and and more exciting.” Institute was founded in 1964 and is located Yakov Sinai has supervised more than 50 academies have elected Sinai to membership in Chernogolovka, some 40 kilometers Ph.D. students. or honorary membership: the American northeast of Moscow; it is at the heart of 2 Dennis Kosygin, as quoted in The Daily Princetonian, 1 Bulletin (New Series) of the American Mathematical