The Laureates

Copyright © Klaus Tschira Stiftung / Peter Badge

Yakov G. Sinai

Born 21 September 1935 in Moscow (Russia)

Abel-Prize (2014) “for his fundamental contributions to dynamical systems, ergodic theory, and mathematical physics”

Yakov G. Sinai comes from a family of scientists: both his parents worked as researchers in microbiology, his grandfather was the Head of the Institute of Differential Geometry at the State University in Moscow. Sinai received his doctorate 1960/63, advised by Andrej Kolmogorov (1903-1987), one of the leading brains behind modern probability theory. Between 1960 and 1971 he did research at the Laboratory for Probabilistic and Statistical Methods at the State University Moscow, where in 1971, he accepted a professorship. At the same time he worked as Senior Researcher at the Landau Institute for Theoretical Physics at the Russian Academy of Sciences. In 1993 he became Professor of Mathematics at the University of Princeton (USA), whilst still continuing his work for the Landau Institute for Theoretical Physics. In 1997/1998, Sinai was appointed Thomas Jones Professor in Princeton and in 2005 a Moore Distinguished Scholar at the California Institute of Technology in Pasadena, California.

Yakov Sinai is author of more than 250 books and research papers, some of which he wrote together with his wife Elena B. Vul, a mathematician. (She is also coming from a family of scientists: her father was a famous physicist.) Besides the Abel Prize, Sinai has received many awards, for instance the Boltzmann Gold Medal from the Commission for Statistical Physics of the International Union of Pure and Applied Physics (1986) and the Dirac Medal from the Abdus Salam International Centre for Theoretical Physics in Trieste (1992); he was honored with the Wolf Prize in Mathematics (1997), the Nemmers Prize in Mathematics (2002), the Henri-Poincaré-Prize from the International Association of Mathematical Physics (2009) and the Dobrushin International Price of the Institute for Information Transmission of the Russian Academy of Sciences (2009). In 2013 he received the Leroy P. Steele Prize for Lifetime Achievement from the American Mathematical Society. Yakov Sinai is also member of many scientific academies and holds four honorary degrees.

Yakov Sinai works in the field of probability theory and dynamical systems. These are mathematical systems which are developing from an initial state, while the development depends solely on the initial state but not on the starting time. Many physical processes can be seen as dynamical systems, for instance oscillating pendula or the movement of planets in space. Some dynamical systems are extremely sensitive to small changes of the initial state, sometimes they may even behave at random.

In the 1920s and 1930s, mathematicians especially in Russia began to study dynamical systems in a systematic way. Subsequently the question arose whether a way could be found to sort or categorize dynamical systems. Sinai, who was in the 1950s a student of Kolmogorov, found indeed a method to do so: he succeeded in assigning a kind of invariant “fingerprint” — an entropy — to certain dynamical systems. The Kolmogorov-Sinai entropy measures the influence of randomness in the development of a system and therefore specifies how predictable the system is.

The Kolmogorov-Sinai entropy turned out to be an extremely useful tool, for example to analyse Bernoulli-Schemes. A Bernoulli-Scheme could be described as a set of all possible series of n coin tosses, where the coin has a certain probability p to show head (and it shows tails otherwise). In 1970, Daniel Ornstein could show by the means of Sinai’s notion of entropy that such sets of series of heads and tails never appear completely the same for different values of p.

However, the Kolmogorow-Sinai entropy is only one example for the many mathematical tools Sinai has defined and studied over the years. Famous are also the Sinai billards, dynamical systems that can be illustrated as billiard games on quadratic tables that have a round cushion in the middle. In statistical mechanics, the Pirogov-Sinai theory became influential to study phase images of low temperature spin models. Together with David Ruelle (*1935) and Rufus Bowen (1947-1978), Sinai also discovered a new notion of measure to characterize dissipative systems with chaotic behavior — such as the chaotic formation of structures on the surface of the sun.