Pierre Deligne
Institute for Advanced Study
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Primary Section: 11, Mathematics Membership Type:
International Member
(elected 2007)
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Research Interests
My home is algebraic geometry, a discipline connected to many others; wherever polynomials appear, it can be there to provide a geometric understanding. For instance: diophantine equations (solutions of equations in integers or rationals), identities between integrals with algebraic integrands, algebraic groups. I am fascinated by the multiplicity of cohomology theories algebraic varieties give rise to, and their interrelation. I constructed one: mixed Hodge theory. Thanks to their properties, spaces and maps coming from algebraic geometry are very special. A grandiose theory of Grothendieck ("motives") makes sense of it, modulo conjectures which remain inaccessible. Some of my works give unconditional variants sufficients for some applications. I have also worked with automorphic forms (related with the arithmetic and the cohomology of algebraic varieties by Langlands philosophy), with configurations of hyperplanes, tensor categories, multizeta values (a story beginning with Euler).
