[Todos CMAT] Premio a Y. Sinai
roma en fing.edu.uy
roma en fing.edu.uy
Jue Ene 3 08:36:25 UYST 2013
LEROY P. STEELE PRIZE FOR LIFETIME ACHIEVEMENT
The Leroy P. Steele Prizes were established in 1970 in honor of George
David Birkhoff, William Fogg Osgood, and William Caspar Graustein and
are endowed under the terms of a bequest from Leroy P. Steele. Prizes
are awarded in up to three categories and each is awarded annually.
The following citation describes the award for Lifetime Achievement.
Citation
Yakov Sinai
The 2013 Steele Prize for Lifetime Achievement is awarded to Yakov Sinai for
his pivotal role in shaping the theory of dynamical systems and for his
groundbreaking contributions to ergodic theory, probability theory,
statistical mechanics, and mathematical physics.
Sinai?s research exhibits a unique combination of brilliant analytic
technique,
outstanding geometric intuition, and profound understanding of underlying
physical phenomena. His work highlights deep and unexpected
connections between
dynamical systems and statistical mechanics. Sinai has opened up new
directions,
including Kolmogorov?Sinai entropy, Markov partitions, and Sinai?Ruelle?Bowen
measures in the hyperbolic theory of dynamical systems; dispersing billiards,
a rigorous theory of phase transitions in statistical mechanics and space-time
chaos. In addition, Sinai has made seminal contributions in the theory of
Schrödinger operators with quasi-periodic potentials, random walks in random
environments, renormalization theory, and statistical hydrodynamics
for Burgers
and Navier?Stokes equations.
Sinai pioneered the study of dispersing billiards: dynamical systems
which model
the motion of molecules in a gas. The simplest example of such a
billiard table,
a square with a disk removed from its center, is called ?Sinai?s
billiard.? Studying
billiard motions within the framework of hyperbolic theory, Sinai discovered
that they exhibit deep ergodic and statistical properties (such as the
central limit
theorem). Owing to Sinai?s work, some key laws of statistical
mechanics for the
Lorentz gas can be established with mathematical rigor. In particular,
Sinai made
the ?rst steps towards justi?cation of Boltzmann?s famous ergodic hypothesis,
proposed in the end of the nineteenth century: ?For large systems of
interacting
particles in equilibrium, time averages are close to the ensemble average.?
Sinai returned to this subject several times in the period 1970?90
with various
co-authors, including his students Bunimovich and Chernov. 55
Together with his student Pirogov, Sinai created a general theory of
low-temperature
phase transitions for statistical mechanics systems with a ?nite number of
ground states. Pirogov?Sinai theory forms essentially the basis for modern
equilibrium statistical mechanics in a low-temperature regime.
Sinai made seminal contributions to the theory of random walks in a random
environment. With his model, known nowadays as ?Sinai?s random walk,? he
obtained remarkable results about its asymptotic behavior. With his student
Khanin, Sinai pioneered applications of the renormalization group method
to multi-fractal analysis of the Feigenbaum attractor, and to the Kolmogorov?
Arnold?Moser theory on invariant tori of Hamiltonian systems.
In the past ?fteen years Sinai has brought novel tools and insights from
dynamical systems and mathematical physics to statistical hydrodynamics,
obtaining new results for the Navier?Stokes systems. Speci?cally, along
with D. Li, Sinai devised a new renormalization scheme which allows the
proof of existence of ?nite time singularities for complex solutions of
the Navier?Stokes system in dimension three.
Sinai?s mathematical in?uence is overwhelming. During the past half-century he
has written more than 250 research papers and a number of books.
Sinai?s famous
monograph, Ergodic Theory (with Cornfeld and Fomin), has been an introduction
to the subject for several generations, and it remains a classic.
Sinai supervised more than ?fty Ph.D. students, many of whom have become
leaders in their own right. Sinai?s work is impressive for its breadth.
In addition to its long-lasting impact on pure mathematics, it has played a
crucial role in the creation of a concept of dynamical chaos which has been
extremely important for the development of physics and nonlinear science over
the past thirty-?ve years. The Steele Prize for Lifetime Achievement is
awarded to Sinai in recognition of all these achievements.
Biographical Note
Yakov G. Sinai was born in 1935 in Moscow, Soviet Union, now Russia.
He received his Ph.D. degree (called a Candidate of Science in Russia) and
then his doctorate degree (Doctor of Science) from Moscow State University.
For several years, he combined his position at Moscow State University and the
Landau Institute of Theoretical Physics of the Russian Academy of Sciences.
Since 1993, he has been a professor in the mathematics department of Princeton
University.
Ya. Sinai received various honors recognizing his contributions. He was
elected as a foreign associate of the National Academy of Sciences and a
foreign member of the Academy of Arts and Sciences. He is a full member
of the Russian Academy of Sciences, and he was recently elected as a
foreign member of the Royal Society in London. He is also a member of
the Brazilian Academy of Science, the Hungarian Academy of Science,
the Polish Academy of Science, and Academia Europea.56 Among his other
recognitions are the Wolf Prize in Mathematics, the Nemmers Prize, the
Lagrange Prize, the Boltzmann Medal, the Dirac Medal, and the Poincaré Prize.
Response from Yakov Sinai
It is a great honor to be awarded the Steele Prize for Lifetime Achievement
from the American Mathematical Society. I worked in several directions
in mathematics, including the theory of dynamical systems, statistical
and mathematical physics, and probability theory. My mentors who had a big
in?uence on me were A. N. Kolmogorov, V. A. Rokhlin, and E. B. Dynkin.
I also bene?tted a lot from many contacts with my colleagues.
I was very fortunate to have talented students, many of whom became strong
and famous mathematicians. Unfortunately, it is not possible to list the names
of all of them here. I thank my family and friends for their encouragement and
support. Finally, I thank the selection committee for its work.
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