Abel Prize for Belgian Pierre Deligne

March 20, 2013 08:36 pm | Updated November 18, 2016 01:19 pm IST - New Delhi:

Belgian mathematician >Pierre Deligne , who is regarded as one of the most celebrated mathematicians of the 20th century, has been chosen for this year’s prestigious Abel Prize in Mathematics. The 69-year-old professor emeritus of the Institute of Advanced Study, Princeton, is being awarded for his “seminal contributions to algebraic geometry and for their transformative impact on number theory, representation theory and related fields.”

President of the Norwegian Academy of Sciences and Letters (which instituted this award in 2002) Kristi Strøm Bull announced the award at the academy in Oslo on Wednesday. The Abel Prize is considered equivalent to the Nobel Prize, which is not awarded in the field of mathematics. It carries a cash award of 6 million Norwegian krone (about €800,000 or $1 million). The prize will be given by His Majesty King Harald V of Norway at an award ceremony in Oslo on May 21.

The prize, which was given for the first time in 2003, recognises contributions of extraordinary depth and influence in mathematical sciences. In awarding the prize to Professor Deligne, the committee noted: “Deligne’s powerful concepts, ideas, results and methods continue to influence the development of algebraic geometry as well as mathematics as a whole.”

Geometric objects like lines, circles and spheres can be described by simple algebraic equations. This fundamental link between algebra and geometry led to the development of the branch of mathematics called algebraic geometry, in which geometric methods are used to study solutions of polynomial equations. Conversely, algebraic techniques can also used to analyse geometric objects.

Developments in the field over the years, particularly in the 20th century, have given modern algebraic geometry a central place in mathematics because of its deep connections to almost every area of mathematics. It has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory. By finding connections between various fields of mathematics, Prof. Deligne’s contributions have played a crucial role in many of these developments.

Prof. Deligne’s research has led to several important discoveries. One of his most famous contributions was his spectacular proof of the last and the deepest of the (André) Weil conjectures in 1973, for which he was awarded the Fields Medal in 1978 and the Crafoord Prize in 1988, the latter jointly with Alexander Grothendieck.

Prof. Deligne’s solution of the Weil conjectures made him famous in the world of mathematics at a very young age. Research works by others that followed this demonstrate the extreme variety as well as the difficulty of the techniques involved and the inventiveness of his methods. His best known works relate to algebraic geometry and number theory.

A highly influential mathematician, Prof. Deligne has a number of mathematical concepts named after him: the Deligne Conjecture, the Deligne-Mumford moduli of algebraic curves, Deligne-Mumford stacks and Deligne cohomology, to name a few.

“All manner of outstanding results would not have been possible without the prior work and insight provided by Deligne, such as Gerd Falting’s proof of Mordell’s conjecture, Andrew Wiles’ proof of Fermat’s Last Theorem (and the Shimura-Taniyama conjecture), Vladimir Voevodsky’s work on John Milnor’s conjecture and the Khare-Wintenberger’s proof of Jean-Pierre Serre’s conjecture,” says Kapil Paranjape, an algebraic geometer at the Indian Institute for Science Education and Research (IISER), Mohali.

“In particular, his proofs (he gave two proofs!) of the Weil conjecture (and Ramanujan’s conjecture on the tau function as a consequence) stand out both for the beauty and insight that these proofs provided into the links between arithmetic and geometry,” Mr. Paranjape said.

Prof. Deligne came to Princeton in 1984 from the Institut des Hautes Études Scientifique (IHES), in Bures-sur-Yvette near Paris, where he was appointed its youngest-ever permanent member in 1970. His father had wanted him to become an engineer and pursue a career that would afford him a good living. But he decided to do what he loved, which was mathematics. He went to the University of Brussels where, as a student of Jacques Tits, Prof. Deligne was pleased to discover, as he says, that “one could earn one’s living by playing; that is, by doing research in mathematics.”

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