Conceptual strength and ageless beauty

Kristian Seip, the chairman of the Abel Committee, gave this speech just after the announcement at the Norwegian Academy of Science and Letters 22. March:
Mr. President, ladies and gentlemen: The Abel Prize for 2007 is awarded to Srinivasa S. R. Varadhan for his fundamental contributions to probability theory and in particular for creating a unified theory of large deviations. Probability theory is the mathematical tool for analyzing situations governed by chance. Systems in the real world will almost always be subject to what we at best can comprehend as random effects. Thus, probability theory is one of the foundations of modern science, technology and economics. The law of large numbers was discovered by Jacob Bernoulli early in the eighteenth century. This law shows that the average outcome of a long sequence of coin tosses is usually close to the expected value. Yet, as we all know, the unexpected happens, and the question is: how? The theory of large deviations studies the occurrence of rare events and has concrete applications to fields as diverse as physics, biology, economics, statistics, computer science, and engineering. The law of large numbers states that the probability of a deviation beyond a given level goes to zero. However, for practical applications, it is crucial to know how fast it vanishes. For example, what capital reserves are needed to keep the probability of default of an insurance company below acceptable levels? In analyzing such actuarial “ruin problems”, the Swedish mathematician and statistician Harald Cramér discovered in 1937 that standard approximations based on the Central Limit Theorem (as visualized by the bell curve) are actually misleading. He then found the first precise estimates of large deviations. It took 30 years before Varadhan discovered the underlying general principles and began to demonstrate their tremendous scope. Varadhan’s theory of large deviations, partly worked out in collaboration with Monroe D. Donsker, provides a unifying and efficient method for clarifying a rich variety of phenomena arising in complex stochastic systems, in fields as diverse as quantum field theory, statistical physics, population dynamics, econometrics and finance, and traffic engineering. It has also greatly expanded our ability to use computers to simulate and analyze the occurrence of rare events. Over the last four decades, the theory of large deviations has become a cornerstone of modern probability theory. Varadhan has made key contributions in several other areas of probability theory. In joint work with Daniel W. Stroock, he developed a martingale method for characterizing diffusion processes. This new approach turned out to be an extremely powerful way of constructing Markov processes, for example of the type that arise in population genetics. Varadhan has also made important contributions to the analysis of hydrodynamical limits describing the macroscopic behaviour of very large systems of interacting particles. His ideas also had a strong influence on the analysis of random walks in a random environment. His name is now attached to the method of “viewing the environment from the travelling particle”, one of the few general tools in the field. Varadhan's work has great conceptual strength and ageless beauty. His ideas have been hugely influential and will continue to stimulate further research for a long time.

Yves Meyer received the Abel Prize from H.M. King Harald

H.M. King Harald presented the Abel Prize to Yves Meyer of the École normale supérieure Paris-Saclay, France at an award ceremony in Oslo on 23 May. He receives the prize for his pivotal role in the development of the mathematical theory of wavelets, says John Rognes, chair of the Abel committee. Among the prominent guests attending the award  ceremony was the French ambassador to Norway, Jean-François Dobelle and the Norwegian Minister of Education and Research, Torbjørn Røe Isaksen.

(26.05.2017) More

Three days of celebration for Abel Laureate Yves Meyer

His Majesty King Harald will present the Abel Prize to Yves Meyer at an award ceremony in Oslo on 23 May. He receives the prize "for his pivotal role in the development of the mathematical theory of wavelets", to quote the Abel committee. Yves Meyer, of the École  normale supérieure Paris-Saclay, was the visionary leader in the modern development of this theory, at the intersection of mathematics, information technology and computational science.

(12.05.2017) More

The Abel lectures 2017

Abel Laureate Yves Meyer gave his prize lecture at the University of Oslo on the 24th of May, with following Abel lectures by Stéphane Mallat, Ingrid Daubechies og Emmanuel Jean Candès. Watch the lectures here.

(08.05.2017) More

Congratulations from AMS President

"On behalf of the American Mathematical Society, it is my great pleasure to congratulate Professor Yves Meyer, recipient of the 2017 Abel Prize.  Professor Meyer has been a visionary in a broad range of fields, including number theory and differential equations.  His fundamental work in the theory of wavelets has transformed the world of signal processing and has led to a myriad of practical applications."  -- AMS President Kenneth A. Ribet (University of California, Berkeley)
Photo: Jim Brook

 

(02.04.2017) More

Yves Meyer receives the Abel Prize

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2017 to Yves Meyer (77) of the École normale supérieure Paris-Saclay, France “for his pivotal role in the development of the mathematical theory of wavelets”. The President of the Norwegian Academy of Science and Letters, Ole M. Sejersted, announced the winner of the 2017 Abel Prize at the Academy in Oslo today, 21 March.

Yves Meyer was the visionary leader in the modern development of this theory, at the intersection of mathematics, information technology and computational science. 

Wavelet analysis has been applied in a wide variety of arenas as diverse as applied and computational harmonic analysis, data compression, noise reduction, medical imaging, archiving, digital cinema, deconvolution of the Hubble space telescope images, and the recent LIGO detection of gravitational waves created by the collision of two black holes.

Yves Meyer will receive the Abel Prize from His Majesty King Harald V at an award ceremony in Oslo on 23 May.

The Abel Prize recognizes contributions of extraordinary depth and influence to the mathematical sciences and has been awarded annually since 2003. It carries a cash award of 6 million NOK (about 675,000 Euro or 715,000 USD). 

(21.03.2017) More
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