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AWARD CEREMONY 2014

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CMYK The Abel Prize Award Ceremony May 20, 2014 The University Aula, Oslo

Procession accompanied by the “Abel Fanfare” (Klaus Sandvik) Performed by musicians from The Staff Band of the Norwegian Armed Forces

His Royal Highness Crown Prince Haakon enters the University Aula

Improvisations on Bulgarian traditional music Stian Carstensen, accordeon

Opening speech by Professor Nils Chr. Stenseth President of The Norwegian Academy of Science and Letters

Sea-Shell Music: Carl Engel

The Abel Committee’s Citation by Professor Ragni Piene Chair of the Abel Committee

His Royal Highness Crown Prince Haakon presents the Abel Prize to Yakov G. Sinai

Acceptance speech by Abel Laureate Yakov G. Sinai

Baroque Bach Mountain Music: Trad./Gammalgrass

His Royal Highness Crown Prince Haakon leaves the University Aula

Procession leaves

The Prize Ceremony will be followed by a reception at Midtgolvet in Det Norske Teatret. During the reception, Yakov Sinai will be interviewed by Tonje Steinsland. More info on page 15. the most bridges connecting the world of deterministic (dynamical) systems with the Professor Yakov G. Sinai world of probabilistic (stochastic) systems. Perhaps it is only to be expected that he Princeton University, USA, and Landau Institute for Theoretical Physics, Russian is the author of an article titled “Mathematicians and Physicists = Cats and Dogs?” Academy of Sciences During the past half-century Yakov Sinai has written more than 250 research papers Abel Laureate 2014 and a number of books. Sinai and his wife Elena B. Vul, a mathematician and physi- cist, have also written a number of joint papers. Yakov Sinai has supervised more “for his fundamental contributions to dynamical systems, ergodic than 50 Ph.D. students. The deep contributions made by Sinai early in his career theory, and mathematical physics” led to his being invited to lecture at the International Congress of Mathematicians in Yakov G. Sinai was born on 21 Stockholm in 1962. In 2001 he was appointed Chairman of the Fields Medal Com- September 1935 in Moscow, Russia. mittee of International Mathematical Union Both of his parents, Gregory Sinai and Nadezda Kagan, were microbiologists Yakov Sinai has received many distinguished international awards. In 2013 he was with research careers. His grandfa- awarded the Leroy P. Steele Prize for Lifetime Achievement from the American ther, the mathematician Benjamin Mathematical Society. Other awards include the Wolf Prize in Mathematics (1997), Fedorovich Kagan, was head of the the Nemmers Prize in Mathematics (2002), the Henri Poincaré Prize from the Department of Differential Geometry at ­International Association of Mathematical Physics (2009) and the Dobrushin Interna- Moscow State University. Kagan had tional Prize from the Institute of Information Transmission of the Russian Academy of great influence on his grandson. Yakov Sciences (2009). Among his many recognitions are the Boltzmann Gold Medal from Sinai received his B.S. (1957), his Ph.D. the Commission on Statistical Physics of the International Union of Pure and Applied (1960), and his doctorate (1963) from Physics (1986) and the Dirac Medal from the Abdus Salam International Centre for Moscow State University. His advisor Theoretical Physics in Trieste (1992). was the prominent Andrey Kolmogorov. Sinai was a Scientific Researcher at the Many mathematical societies and academies have elected Sinai to membership or Photo: Princeton University/Department of mathematics Laboratory of Probabilistic and Statisti- honorary membership: the American Academy of Arts and Sciences (1983), the cal Methods at Moscow State University from 1960 to 1971. In 1971 he became Russian Academy of Sciences (1991), the London Mathematical Society (1992), a Professor at Moscow State University and a Senior Researcher at the Landau the Hungarian Academy of Sciences (1993), the United States National Academy of Institute of Theoretical Physics, Russian Academy of Sciences. Since 1993 he has Sciences (1999), the Brazilian Academy of Sciences (2000), the Academia Europaea been a Professor of Mathematics at Princeton University, USA, but has concurrently (2008), the Polish Academy of Sciences (2009) and the Royal Society of London kept his position at the Landau Institute of Theoretical Physics. (2009).

Yakov Sinai is one of the most influential mathematicians of the twentieth century. He Professor Sinai is also respected as a teacher at Princeton. In the words of a former has achieved numerous groundbreaking results in the theory of dynamical sys- student, “It’s quite inspirational to be in his class … People feel an immediate urge to tems, in mathematical physics and in probability theory. Many mathematical results participate – there is a radiance which comes from him and inspires us.” He is also are named after him, including Kolmogorov-Sinai entropy, Sinai's billiards, Sinai's known for his persistence in the face of obstacles, be they bureaucratic or theoreti- random walk, Sinai-Ruelle-Bowen measures, and Pirogov-Sinai theory. Sinai is highly cal, a trait which has served him well throughout the years. respected in both physics and mathematics communities as the major architect of

4 5 this type of cooperation with the public sector - cooperation with a long-term perspec- Professor Nils Chr. Stenseth tive.

President of The Norwegian Academy of Science and Letters Most of all, the Abel Prize – and the prize winners – shall give inspiration to other math- Your Royal Highness, Minister, Your Excellencies, ematicians and aspiring mathematicians and to young people with talent in mathemat- Dear Abel Prize Laureate Professor Yakov G. Sinai, ics. The prize winner will be - as he/she should be – a role model for talented young Dear friends of long-term, basic research, ladies and researchers. Starting last year, this role model role has been systematised through ­gentlemen, The Heidelberg Laureate Forum. Young researchers from around the whole world are invited to this forum to meet former recipients of four important prizes in mathemat- ics and computer science: the Abel Prize, the Fields Medal, the Turing Award and the On behalf of The Norwegian Academy of Science and Letters, it is a great joy and Nevanlinna Prize. This is a splendid example of interaction between market and cathe- honour for me to welcome you to this year’s Abel Prize Award Ceremony. dral - the business community and academia. We need more people who can help to highlight this kind of top-level research and thereby encourage even more outstanding research of this sort. I would like to thank the German entrépreneur, Dr. Klaus Tschira, The Abel Prize has several main objectives: First, it shall give distinction to mathemati- for having taken the initiative to launch this forum and for having established a fund that cians who have made a fundamental contribution to the development of the field of will ensure the future of these events where former prize winners and talented young mathematics. Second, the prize – and the prize winners – shall inspire the research researchers from around the whole world can meet - to their mutual inspiration. community in general and mathematicians throughout the world in particular. Third, through the example set by the recipient of the prize, it shall motivate young people to become involved in mathematical research – and in the broadest sense convey to Indeed, society is dependent on mathematics at all levels. It is my conviction that the the greater public the importance of basic mathematical research and basic research Abel Prize, with its many activities for young people, and now the annual Heidelberg in general. In the statutes of the Abel Prize, it is written that “The Prize shall help boost Laureate Forum will play a major role in strengthening interest in the subject of math- the status of the field of mathematics in society and stimulate children and youth to ematics among our young people. I will go so far as to assert that this type of prize become interested in mathematics”. and the activities associated with it will improve research's repute and give it a stronger platform in society. Certainly it supports the awareness of this excellent research - exactly the kind of high-level research that we are dependent on in order to further Mathematics is one of the very most important professional disciplines - it is the develop our knowledge-based society and our whole culture. The fact that Oslo's foundation to all of natural science. What’s more, mathematics is extremely important main street, Karl Johan, is festively decorated with Abel banners serves as a fantastic in many other disciplines in addition to the natural sciences. That is why mathematics springboard for calling attention to the importance of outstanding basic research, and demands people's - and the authorities' - attention. the work done by the Abel Board has provided an excellent foundation. New this year is the presentation of two films at Victoria Cinema here in Oslo: «How I came to hate One of the main tasks of the Abel Board is to help realise the whole range of the Abel maths» and «Colors of math», both featuring the mathematician Cédric Villani, himself Prize's intentions by stimulating interest in mathematics among children and youth. a member of the Abel Committee who selects the prize winner. These films will later be One way of doing this is the Norwegian Mathematical Olympiad (the Norwegian Math- shown at the Bergen International Film Festival this autumn. This is promotion of math- ematical Olympis), which is usually just called the Abel Competition. Another way is the ematics at its best. Let me take the opportunity to thank the Abel Board, and not least UngeAbel contest for teams of pupils in ninth grade which was organized for the first its chairman, Professor Helge Holden, for the splendid work that they are doing in order time this year. Contests of this sort are important, but it is even more important to have to reap the benefits of the Abel Prize far beyond the ranks of mathematicians. This is good teachers in the different years of schooling - and at our universities. Nils Henrik your last year as chairman of the Abel Board. We want to thank you for the energy you Abel had an excellent mathematics teacher – Bernt Michael Holmboe. To emphasize have devoted to this work for the benefit of mathematics, and science in general. the important role that teachers play, a teacher is honoured each year with the Holm- boe Memorial Prize. The Abel Prize is a young prize - this year is the twelfth time that it is being awarded. Nevertheless, it has achieved a very high status in the mathematical research com- On behalf of the Norwegian government, the Ministry of Education and Research munity. In my opinion, this success is the direct result of the Abel Prize Committee’s provides financial support to the Abel Prize and to the events associated with the prize. ability to find worthy winners each year – worthy in the sense that there is general The Academy is very grateful for this commitment to increasing the awareness of the international consensus within the field of mathematics that the awards that have been importance of mathematics - and the natural sciences - in today’s society. I would also made have been well deserved. I would therefore like to take this opportunity to thank like to thank Petroleum Geo-Services, PGS, for the support they provide in the form of the Abel Prize Committee, led by Professor Ragni Piene, for their excellent work and a direct financial contribution, not least for the work aimed at school pupils and their dedication. This is your last year as chairman of the Abel Prize Committee; you have efforts to strengthen the mathematics institutions in more financially disadvantaged every reason to be proud of your efforts! countries, e.g. by establishing a mathematics centre in Ghana. This is a magnificent example of the way in which the private sector can help stimulate academic activity If the Abel Prize and equivalent prestigious prizes are presented in the right way, they at different levels. The private sector is greatly dependent on a generally high level of will help strengthen science's and basic research's position and good repute in society, competence in mathematics and the natural sciences. Moreover, it is wonderful to see and it is on this type of science that our knowledge-based society and our entire culture depend. 6 7 7 10

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1. Endre Szemerédi receives the Abel Prize from H.M. King Harald V 8. Wreath-laying ceremony at the Abel Monument 2. Mikhail Gromov and Minister Tora Aasland outside Akershus Castle at the Abel Banquet 9. John Griggs Thompson and Jacques Tits 3. Lennart Carleson is received in audience by H.M. Queen Sonja at the Royal Palace 10. Srinivasa S.R. Varadhan in Karl Johans gate 4. John Milnor interviewed by Tonje Steinsland at Gamle Logen 11. Jean-Pierre Serre, the first Abel Prize Laureate 5. Pierre Deligne gives his Abel Lecture at the University of Oslo 12. Peter D. Lax gives his acceptance speech 13 6. John Torrence Tate inspires young students at Oslo Cathedral School 13. The Abel Prize Award Ceremony at the University Aula 7. Isadore M. Singer and Michael F. Atiyah receive the Abel Prize from H.M. King Harald V One example is the study of a gas in a container. Boltzmann modeled gas molecules Professor Ragni Piene as billiard balls moving at constant speed and colliding with each other and with the Chair of the Abel Committee walls of the container. His hypothesis was that this system is ergodic. Sinai realized that it made sense to study a much simpler situation: one ball moving on a billiard table with an obstruction in the middle, and he verified Boltzmann’s hypothesis in this case. He continued this work with Bunimovich and Chernov.

With Ruelle and Bowen, Sinai discovered an important invariant measure – the SRB Your Royal Highness, dear Minister, Your Excellencies, honored Laureate, dear measure – for certain systems with chaotic behavior. This versatile notion is very useful, colleagues and guests! for example, when trying to understand real-life complex chaotic behavior such as turbulence. The study of Anosov diffeomorphisms helped Sinai understand mixing Many natural phenomena, such as planetary motion, ocean currents, turbulence systems. Other pioneering work by Sinai and his collaborators include: random walks in in air and water, and population dynamics, can be described using mathematical a random environment (Sinai’s walks), phase transitions (with Pirogov), one-dimensional models. Ever since the time of Newton, mathematicians, physicists and engineers turbulence (with E, Khanin and Mazel), the renormalization group theory (with Bleher), have used differential equations to create such models. The models aim at explaining and the spectrum of the Schrödinger operator. the phenomena and predicting how they evolve over time. Some phenomena can be predicted with great accuracy, whereas others seem to evolve in an unpredictable, Sinai has trained and influenced a generation of leading specialists in his research chaotic way. We can predict the movements of a pendulum, but it is hard to tell fields. Much of his research has become a standard toolbox for mathematical precisely how the weather will be in one or two weeks. physicists. His works have had and continue to have a broad and profound impact on mathematics and physics, as well as on the ever fruitful interaction of these two fields. Mathematical models of this kind are called dynamical systems, and they constitute an important part of many areas of mathematics, especially with regard to statistical mechanics and theoretical physics. Intuitively, we distinguish between deterministic and random systems, but it turns out that order and chaos are intimately connected. We may find chaotic behavior in deterministic systems, and conversely, the statistical analysis of chaotic systems may lead to definite predictions.

Yakov Sinai made fundamental contributions in this broad domain. He discovered surprising connections between order and chaos and developed the use of probability and measure theory in the study of dynamical systems. His first remarkable contribution, inspired by his teacher Kolmogorov, was a precise mathematical definition of an invariant of dynamical systems. This invariant is now called Kolmogorov–Sinai entropy, and it has become a key notion expressing the degree of complexity, or unpredictability of a system. This work led to very important advances in the classification of dynamical systems.

The Abel Committee: Cédric Villani, Maria J. Esteban, Stanislav Smirnov, Ragni Piene and Gang Tian . Photo: Eirik Furu Baardsen 10 11 Many people played an important role in my rise as a mathematician. It is my great Professor Yakov G. Sinai pleasure to mention all of them on this special day. My grandfather from my mother’s Acceptance speech side, V.F. Kagan, was the head of the chair in differential geometry at Moscow State University. He worked on the foundations of geometry and had some contact with D. Hilbert. My parents worked in biology. My father-in-law was a famous physicist in Russia and headed the work on semi-conductors in the Soviet Union.

I would like to mention my half-brother, G.I. Barenblatt, who always insisted that my future was in mathematics. Your Royal Highness the Crown Prince of Norway, Excellencies, Minster, President of the Norwegian Academy of Sciences and Letters, Professor Nils Chr. Stenseth, Ladies and As already mentioned, my thesis advisor was A.N. Kolmogorov, who is considered to Gentlemen, be one of the great mathematicians of the 20th century. His role in the development of mathematics deserves a special lecture. The famous Russian mathematician I.M. It is a great honour to be awarded the Abel Prize. The name Abel has been known to ­Gelfand organized a remarkable seminar which was attended by many people of my all mathematicians in the world since the nineteenth century. It calls to mind Abelian generation, the previous generation and younger generations. My first advisor was E.B. groups, Abelian Integrals and many Abelian theorems, which are key concepts of mod- Dynkin, who is now Professor Emeritus at Cornell University. A great role in my educa- ern mathematics. The prestige of the Abel Prize is comparable to that of the Nobel Prize. tion was played by V.A. Rokhlin who was also a close friend. Many people have sent me warm congratulations in connection with this award, in partic- In conclusion, let me say that this is an unforgettable day for my wife and me. ular my colleagues at the Mathematics Department of Princeton University, members of the Landau Institute of Theoretical Physics, many members of the Institute of Information Transmission in Moscow, and many other colleagues, co-authors, and students. This is the kind of support that gives me great inspiration and impetus for future work.

The Landau Institute of Theoretical Physics in Moscow was a special place for me because mathematicians and physicists there learned to understand each other and to work together on problems of mutual interest. The previous generation offered striking examples of mathematicians who made fundamental contributions to physics. Let me mention my advisor, A.N. Kolmogorov and also I.M. Gelfand and N.N. Bogolyubov in Russia and John von Neumann in the USA. The Mathematics Department of the Landau Institute of Theoretical Physics was headed by the great mathematical physicist S.P. Novikov. At that time, physical and mathematical lectures were held equally often. It was new then for mathematicians and physicists to understand and evaluate the results of each other’s work.

Later it became standard throughout the world. Mathematicians such as Gromov, ­Kontsevich, Ruelle and others are frequent participants in physics seminars whereas ­Witten, Seiberg, Faddeev and others often attend mathematics seminars. All of this became extremely important for my scientific life.

12 13 Kvernberg received great acclaim for his multifaceted work, “Liarbird”, commissioned by the 2010 The musicians Trondheim Jazzfest and Moldejazz. The recording of “Liarbird” won him the 2011 Spellemann Award for Jazz Album of the Year. Kvernberg received positive reviews for his playing on the 2012 album “The Death Defying Unicorn” by the Trondheim-based band, Motorpsycho. He later joined Motorpsy- cho drummer Kenneth Kapstad in the Kenneth Kapstad Group to perform at the Trondheim Jazzfest in 2010. The quintet changed its name to Grand General prior to the release of their debut album “Grand General” in February 2013.

OLE MORGEN VÅGAN, Bass Since the end of the 90’s, Vågan has played an active role in Norwegian jazz circles as a bass player, composer and band leader. He came into the spotlight through his work as band leader and composer for the ensemble Motif, which he still leads today, ten years after its inception. As one of Norway’s most active bass players, he has been a driving force for young musicians and he has cooperated with well-known artists and musicians both in Norway and abroad. Active as musician since the age of 9, Vågan was considered one of the great talents of his generation. After studies with Mats Eilertsen in his teenage years, he continued his studies at the Trondheim Conservatory of Music (Jazz Dept.). He joined Bugge Wesseltoft’s New Conception of Jazz in the early 2000’s and toured with them for three years. He has composed music for several well-reputed, key orchestras and musicians, for which he has received critical acclaim. He has recorded around 40 albums with various STIAN CARSTENSEN, Pedal steel guitar, accordeon and banjo orchestras, arranged music and contributed to a number of CDs ranging from Balkan music to pop productions, but his main interest remains modern improvised music. Stian Carstensen is a true multi-instrumentalist. He started on the accordion at an early age. In high- school he started playing the guitar, and he was soon playing better than any of his fellow villagers. He was accepted at the Conservatory of Music in Trondheim in the Department of Jazz. There he was persuaded to take up the accordion again. Stian has released five records with Farmers Market and Reception and interview one solo album. As a musician and producer, he has contributed to about 70 recordings by various artists. He has toured Europe, Asia, South America and the USA with his own projects and with the Tonje Steinsland in conversation with Yakov Sinai saxophonist Michael Brecker and Farmers Market, and he has collaborated with the American singer Mike Patton. Stian wrote lyrics and music for a new Norwegian national anthem for orchestra, choir and vocal soloist, which was commissioned by the Norwegian Broadcasting Corporation in 2008. He won the Spellemann Award in 2008 for the album "Surfin’ USSR” and in 2011 for “Slav To The Rhythm”. For this album, he was also nominated for the best composer award. In 2013, Stian wrote a commissioned work for the 40th anniversary of Vossajazz.

OLA KVERNBERG, Violin Ola Kvernberg began classical studies at an early age, but soon became interested in jazz. He started his jazz studies at the Trondheim Conservatory of Music in 2001, collaborating (at age 18) with Hot Tonje Steinsland interviewed Pierre Deligne in 2013. Club de Norvège guitarist Jimmy Rosenberg. Kvernberg recorded and toured with the Hot Club for several years, and during his student years he also began issuing recordings under his own name. He demonstrated his creative jazz diversity as a member of the Trondheim Jazz Orchestra, and he The Prize Award Ceremony will be followed by a reception at Det Norske Teatret, performed and recorded with his trio, the Ola Kvernberg Trio, releasing the albums “Night Driver” in Kristian IVs g. 8. During the reception, Yakov Sinai will be interviewed by journalist and TV 2006 and “Folk” in 2009. personality Tonje Steinsland. Light refreshments will be served. The event is open for all guests attending the Award Ceremony. 14 15 The Norwegian AcademyofScienceandLetters www.abelprisen.no

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