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Robert Langlands (born the October 6th 1936 with the Canada) is one of the major Mathématicien S of the 20th century and introduced novel ideas and major in Théorie of the numbers and theory of the representations.

It supported its doctorate with the Université Yale in 1960. During the years 1960, it developed the theory of the Séries of Eisenstein introduced by Atle Selberg. In spite of the interest of this work, it did not obtain from permanent station to the Université of Princeton. It then spent a year in Turkey, in a relative insulation, during which it had several important ideas. Its following work had an enormous impact in mathematics (in a famous anecdote, André Weil complained that a conversation with Langlands gave him a headache). He is permanent member of the Institute for Advanced Study since the beginning of the years 1970.

He is the author of the Programme of Langlands, a dense whole of major conjectures connecting the Théorie of the numbers and the theory of the representations.

Langlands understood that the theory of the forms automorphes provides a generalization of the Théorie of the bodies of class, prone exchange of the Algebraic theory of the numbers. With each representation of a Groupe of Welshman a form automorphe must be associated. The logical development of this idea leads to famous the Conjecture of fonctoriality, which modified nature even key questions of the Théorie of the numbers. To give body to these ideas, Jacquet and Langlands developed the idea of the Mathématicien S Russian according to which the theory of the representations is the natural framework for the theory of the forms automorphes. By using all the tools available, they spectacularly succeeded in giving a complete theory of the forms automorphes for the linear general Groupe GL (2) by establishing to the passage some cases of fonctoriality.

Thereafter, Langlands and James Arthur developed the Formule of the traces of Selberg as method of general attack of the fonctoriality.

The conjecture of fonctoriality is still far from being shown, but a particular case (the conjecture octaédrale of Emil Artin, shown by Langlands and Tunnell) was one of the starting points of the work of Andrew Wiles on the conjecture of Taniyama-Shimura and the Dernier theorem of Fermat.

Since the years 1980, it was interested in the Physique in particular with the theories in conformity of the fields.

In 1996, Langlands received the Prix Wolf and the Prix Nemmers in mathematics in 2006 for its work on the program of Langlands.

External bond

  • the work of Robert Langlands

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