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Henri Antoine Gillet (born 8 July 1953, Tangier) is an American mathematician, specializing in arithmetic geometry and algebraic geometry.
Gillet received in 1974 his bachelor's degree from King’s College London and in 1978 his Ph.D. from Harvard University under David Mumford with thesis Applications of Algebraic K-Theory to Intersection Theory. [1] As a postdoc he was an instructor and from 1981 an assistant professor at Princeton University. He became in 1984 an assistant professor, in 1986 an associate professor, and in 1988 a full professor at the University of Illinois at Chicago, where he was from 1996 to 2001 the head of the department of mathematics, statistics, and computer science. He was a visiting scholar at the Tata Institute of Fundamental Research (2006), the Institute for Advanced Study (1987), the IHES (1985, 1986, 1988), in Barcelona, at the Fields Institute in Toronto and at the Isaac Newton Institute (1998). [2]
Gillet's research deals with differential geometry, algebraic und arithmetic geometry, in particular Arakelov theory and algebraic K-theory. He collaborated with Christophe Soulé and Jean-Michel Bismut. Gillet and Soulé proved in 1992 an arithmetic Riemann–Roch theorem.
Gillet was in 2008 a Senior Fellow at the Clay Mathematics Institute and from 1986 to 1989 a Sloan Fellow. He was an Invited Speaker with talk A Riemann-Roch theorem in arithmetic geometry at the International Congress of Mathematicians in Kyōto in 1990. [3] He was from 1994 to 1999 an editor for the American Journal of Mathematics, from 1995 to 1998 for the International Mathematics Research Notices, and from 2003 to 2007 for the Illinois Journal of Mathematics. [2]
André Weil was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was one of the most influential mathematicians of the twentieth century. His influence is due both to his original contributions to a remarkably broad spectrum of mathematical theories, and to the mark he left on mathematical practice and style, through some of his own works as well as through the Bourbaki group, of which he was one of the principal founders.
Alexander Grothendieck was a stateless mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the twentieth century.
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles. It relates the complex analysis of a connected compact Riemann surface with the surface's purely topological genus g, in a way that can be carried over into purely algebraic settings.
Raoul Bott was a Hungarian-American mathematician known for numerous foundational contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem.
The theory of functions of several complex variables is the branch of mathematics dealing with functions defined on the complex coordinate space , that is, n-tuples of complex numbers. The name of the field dealing with the properties of these functions is called several complex variables, which the Mathematics Subject Classification has as a top-level heading.
Pierre René, Viscount Deligne is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, and 1978 Fields Medal.
In mathematics, Serre's multiplicity conjectures, named after Jean-Pierre Serre, are certain purely algebraic problems, in commutative algebra, motivated by the needs of algebraic geometry. Since André Weil's initial definition of intersection numbers, around 1949, there had been a question of how to provide a more flexible and computable theory.
Don Bernard Zagier is an American-German mathematician whose main area of work is number theory. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany. He was a professor at the Collège de France in Paris from 2006 to 2014. Since October 2014, he is also a Distinguished Staff Associate at the International Centre for Theoretical Physics (ICTP).
In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties.
In mathematics, the Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with indices q > 0 are automatically zero. The implications for the group with index q = 0 is usually that its dimension — the number of independent global sections — coincides with a holomorphic Euler characteristic that can be computed using the Hirzebruch–Riemann–Roch theorem.
This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels of generality.
Shou-Wu Zhang is a Chinese-American mathematician known for his work in number theory and arithmetic geometry. He is currently a Professor of Mathematics at Princeton University.
Dennis Parnell Sullivan is an American mathematician known for his work in algebraic topology, geometric topology, and dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Center and is a distinguished professor at Stony Brook University.
In mathematics, Arakelov theory is an approach to Diophantine geometry, named for Suren Arakelov. It is used to study Diophantine equations in higher dimensions.
Jean-Michel Bismut is a French mathematician who has been a professor at the Université Paris-Sud since 1981. His mathematical career covers two apparently different branches of mathematics: probability theory and differential geometry. Ideas from probability play an important role in his works on geometry.
Lucien Serge Szpiro was a French mathematician known for his work in number theory, arithmetic geometry, and commutative algebra. He formulated Szpiro's conjecture and was a Distinguished Professor at the CUNY Graduate Center and an emeritus Director of Research at the CNRS.
Luc Illusie is a French mathematician, specializing in algebraic geometry. His most important work concerns the theory of the cotangent complex and deformations, crystalline cohomology and the De Rham–Witt complex, and logarithmic geometry. In 2012, he was awarded the Émile Picard Medal of the French Academy of Sciences.
Christophe Soulé is a French mathematician working in arithmetic geometry.
Mark Lee Green is an American mathematician, who does research in commutative algebra, algebraic geometry, Hodge theory, differential geometry, and the theory of several complex variables. He is known for Green's Conjecture on syzygies of canonical curves.
Otto Forster is a German mathematician.
