Pierre Deligne

He completed his doctorate at the University of Paris-Sud in Orsay 1972 under the supervision of Alexander Grothendieck, with a thesis titled Théorie de Hodge.

Starting in 1965, Deligne worked with Grothendieck at the Institut des Hautes Études Scientifiques (IHÉS) near Paris, initially on the generalization within scheme theory of Zariski's main theorem.

Deligne's contribution was to supply the estimate of the eigenvalues of the Frobenius endomorphism, considered the geometric analogue of the Riemann hypothesis.

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.

With Alexander Beilinson, Joseph Bernstein, and Ofer Gabber, Deligne made definitive contributions to the theory of perverse sheaves.

It was also used by Deligne himself to greatly clarify the nature of the Riemann–Hilbert correspondence, which extends Hilbert's twenty-first problem to higher dimensions.

Prior to Deligne's paper, Zoghman Mebkhout's 1980 thesis and the work of Masaki Kashiwara through D-modules theory (but published in the 80s) on the problem have appeared.

In 1974 at the IHÉS, Deligne's joint paper with Phillip Griffiths, John Morgan and Dennis Sullivan on the real homotopy theory of compact Kähler manifolds was a major piece of work in complex differential geometry which settled several important questions of both classical and modern significance.

Other important research achievements of Deligne include the notion of cohomological descent, motivic L-functions, mixed sheaves, nearby vanishing cycles, central extensions of reductive groups, geometry and topology of braid groups, providing the modern axiomatic definition of Shimura varieties, the work in collaboration with George Mostow on the examples of non-arithmetic lattices and monodromy of hypergeometric differential equations in two- and three-dimensional complex hyperbolic spaces, etc.