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Pierre Deligne attended the Free University of Brussels receiving his licence in mathematics in 1966. He continued to study for his doctorate which was awarded in 1968.
Before the award of his doctorate, Deligne was a junior scientist at the Belgium National Foundation for Scientific Research in 1967-68. In 1968 he went to the Institut des Hautes Etudes Scientifiques at Bures-sur-Yvette in France where he was a visiting member until 1970 when he became a permanent member of the Institute.
Deligne remained based at the Institut des Hautes Etudes Scientifiques until 1984 when he went to the Institute for Advanced Study at Princeton where he was appointed a professor.
André Weil gave for the first time a theory of varieties defined by equations with coefficients in an arbitrary field, in his Foundations of Algebraic Geometry (1946). This used Zariski's ideas and also made good use of geometric concepts. Weil's work on polynomial equations led to questions on what properties of a geometric object can be determined purely algebraically.
Weil's work related questions about integer solutions to polynomial equations to questions in algebraic geometry. He conjectured results about the number of solutions to polynomial equations over the integers using intuition on how algebraic topology should apply in this novel situation. The third of his conjectures was a generalisation of the Riemann hypothesis on the zeta function. These problems quickly became major research challenges to mathematicians.
A solution of the three Weil conjectures was given by Deligne. This work brought together algebraic geometry and algebraic number theory and it led to Deligne being awarded a Fields Medal at the International Congress of Mathematicians in Helsinki in 1978. A solution to these problems required the development of a new kind of algebraic topology.
Deligne has worked on many other important problems. The areas on which he has worked, in addition to algebraic geometry, are Hilbert's 21st problem, Hodge theory, theory of moduli, modular forms, Galois representations, L-series and the Langlands conjectures, and representations of algebraic groups.
In addition to the Fields Medal, Deligne was awarded the Crafoord Prize of the Royal Swedish Academy of Sciences in 1988:-
... for his fundamental research in algebraic geometry.
References (4 books/articles)
References elsewhere in this archive:
P R Deligne won a Fields Medal in 1978. You can see a history of the Fields Medal and a list of winners.
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