Pierre Deligne, March 2005

Pierre René, Viscount Deligne (born 3 October 1944 in Brussels) is a Belgian mathematician. Events 42 BC - First Battle of Philippi: Triumvirs Mark Antony and Octavian fight an indecisive battle with Caesar's Year 1944 ( MCMXLIV) was a Leap year starting on Saturday (link will display full calendar of the Gregorian calendar. Brussels (Bruxelles pronounced; Brussel pronounced) officially the Brussels Capital-Region, is The Kingdom of Belgium is a Country in northwest Europe. It is a founding member of the European Union and hosts its headquarters as well as those A mathematician is a person whose primary area of study and research is the field of Mathematics. He is known for fundamental work on the Weil conjectures, leading finally to a complete proof in 1973. In Mathematics, the Weil conjectures, which had become theorems by 1974 were some highly-influential proposals from the late 1940s by André Weil on the He was born in Brussels, and studied at the Universite Libre de Bruxelles (ULB). Brussels (Bruxelles pronounced; Brussel pronounced) officially the Brussels Capital-Region, is The Université Libre de Bruxelles (or ULB) is a French -speaking University in Brussels

After completing a doctorate, he worked with Alexander Grothendieck at the Institut des Hautes Études Scientifiques (IHÉS) near Paris, initially on the generalisation within scheme theory of Zariski's main theorem. A doctorate is an Academic degree that indicates the highest level of academic achievement Experimental infobox see Wikipedia talkPersondata before changing --> Alexander Grothendieck (born March 28, 1928 in Berlin, Germany The Institut des Hautes Études Scientifiques ( IHÉS, en Institute of Advanced Scientific Studies is a French institute supporting advanced research in Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city In Mathematics, a scheme is an important concept connecting the fields of Algebraic geometry, Commutative algebra and Number theory. In Algebraic geometry, a field in Mathematics, Zariski's main theorem, or Zariski's connectedness theorem, is a theorem proved by which implies that fibers He worked closely with Jean-Pierre Serre, leading to important results on the l-adic representations attached to modular forms, and the conjectural functional equations of L-functions. In Mathematics, a modular form is a (complex Analytic function on the Upper half-plane satisfying a certain kind of Functional equation and In Mathematics or its applications a functional equation is an Equation expressing a relation between the value of a function (or functions at a point with its values The theory of L -functions has become a very substantial and still largely Conjectural, part of contemporary Number theory. He also collaborated with David Mumford on a new description of the moduli spaces for curves: this work has been much used in later developments arising from string theory. David Bryant Mumford (born 11 June 1937) is a Mathematician known for distinguished work in Algebraic geometry, and then for research into In Algebraic geometry, a moduli space is a geometric space (usually a scheme or an Algebraic stack) whose points represent algebro-geometric objects of String theory is a still-developing scientific approach to Theoretical physics, whose original building blocks are one-dimensional extended objects called strings

From 1970 until 1984, when he moved to the Institute for Advanced Study in Princeton, Deligne was a permanent member of the IHÉS staff. The Institute for Advanced Study, located in Princeton New Jersey, United States is a center for theoretical research During this time he did much important work, besides the proof of the Weil conjectures: in particular with George Lusztig on the use of étale cohomology to construct representations of finite groups of Lie type, and with Rapoport on the moduli spaces from the 'fine' arithmetic point of view, with application to modular forms. George (Gheorghe Lusztig (born 1946 is a Romanian born American Mathematician. In Mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological In Mathematics, a group of Lie type G(k is a (not necessarily finite group of rational points of a reductive Linear algebraic group G with In Mathematics, a modular form is a (complex Analytic function on the Upper half-plane satisfying a certain kind of Functional equation and He received a Fields Medal in 1978. The Fields Medal is a prize awarded to two three or four Mathematicians not over 40 years of age at each International Congress of the International Mathematical

In terms of the completion of some of the underlying Grothendieck program of research, he defined absolute Hodge cycles, as a surrogate for the missing and still largely conjectural theory of motives. In Algebraic geometry, a motive (or sometimes motif) refers to 'some essential part of an Algebraic variety ' This idea allows one to get around the lack of knowledge of the Hodge conjecture, for some applications. The Hodge conjecture is a major unsolved problem in Algebraic geometry which relates the Algebraic topology of a Non-singular complex Algebraic He reworked the tannakian category theory in his paper for the Grothendieck Festschrift, employing Beck's theorem – the Tannakian category concept being the categorical expression of the linearity of the theory of motives as the ultimate Weil cohomology. In Mathematics, a tannakian category is a particular kind of Monoidal category C, equipped with some extra structure relative to a given field In Category theory, a branch of Mathematics, Beck's monadicity theorem asserts that a Functor U C \to D is All this is part of the yoga of weights, uniting Hodge theory and the l-adic Galois representations. In Mathematics, Hodge theory is one aspect of the study of the Algebraic topology of a Smooth manifold M. The Shimura variety theory is related, by the idea that such varieties should parametrize not just good (arithmetically interesting) families of Hodge structures, but actual motives. In mathematics a Shimura variety is an analogue of a Modular curve, and is (roughly a quotient of an Hermitian symmetric space by a Congruence subgroup This theory isn't yet a finished product – and more recent trends have used K-theory approaches. In Mathematics, K-theory is a tool used in several disciplines

He was awarded the Fields Medal in 1978, the Crafoord Prize in 1988, the Balzan Prize in 2004 and the Wolf Prize in 2008. The Fields Medal is a prize awarded to two three or four Mathematicians not over 40 years of age at each International Congress of the International Mathematical The annual Crafoord Prize is a science prize established in 1980 by Holger Crafoord, a Swedish industrialist and his wife Anna-Greta Crafoord The International Balzan Prize Foundation awards four annual monetary prizes to people or organisations who have made outstanding achievements in the fields of humanities natural

In 2006 he was ennobled by the Belgian king as viscount. ^[1]

Selected publications

• Deligne, Pierre (1974). "La conjecture de Weil: I". Publications Mathématiques de l'IHÉS 43: 273–307.  
• Deligne, Pierre (1980). "La conjecture de Weil: II". Publications Mathématiques de l'IHÉS 52: 137–252.  
• Deligne, Pierre; Mostow, G. Daniel (1993). Commensurabilities among Lattices in PU(1,n). Princeton, N. J. : Princeton University Press. ISBN 0691000964.  

See also

• Deligne conjecture
• Deligne-Mumford moduli space of curves
• Deligne cohomology

References

External links

• O'Connor, John J. Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. Events 390 BC - Roman - Gaulish Wars Battle of the Allia - a Roman army is defeated by raiding Gauls, & Robertson, Edmund F. , “Pierre Deligne”, MacTutor History of Mathematics archive 
• Pierre Deligne at the Mathematics Genealogy Project