Jean-Pierre Serre is a French mathematician who has made contributions to algebraic topology, algebraic geometry and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inaugural Abel Prize in 2003.
Oscar Zariski was an American mathematician. The Russian-born scientist was one of the most influential algebraic geometers of the 20th century.
In mathematics, Serre's multiplicity conjectures, named after Jean-Pierre Serre, are certain 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, which Serre sought to address. In 1958, Serre realized that classical algebraic-geometric ideas of multiplicity could be generalized using the concepts of homological algebra.
Serge Lang was a French-American mathematician and activist who taught at Yale University for most of his career. He is known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He received the Frank Nelson Cole Prize in 1960 and was a member of the Bourbaki group.
Jean Alexandre Eugène Dieudonné was a French mathematician, notable for research in abstract algebra, algebraic geometry, and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendieck, and as a historian of mathematics, particularly in the fields of functional analysis and algebraic topology. His work on the classical groups, and on formal groups, introducing what now are called Dieudonné modules, had a major effect on those fields.
Yuri Ivanovich Manin was a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.
Joseph Hillel Silverman is a professor of mathematics at Brown University working in arithmetic geometry, arithmetic dynamics, and cryptography.
In mathematics, Clifford's theorem on special divisors is a result of William K. Clifford on algebraic curves, showing the constraints on special linear systems on a curve C.
Joseph Daniel Harris is the Higgins Professor of Mathematics at Harvard University. He specializes in the field of algebraic geometry. After earning an AB from Harvard College he continued at Harvard to study for a PhD under Phillip Griffiths.
Phillip Augustus Griffiths IV is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He is a major developer in particular of the theory of variation of Hodge structure in Hodge theory and moduli theory, which forms part of transcendental algebraic geometry and which also touches upon major and distant areas of differential geometry. He also worked on partial differential equations, coauthored with Shiing-Shen Chern, Robert Bryant and Robert Gardner on Exterior Differential Systems.
Robin Cope Hartshorne is an American mathematician who is known for his work in algebraic geometry.
Claire Voisin is a French mathematician known for her work in algebraic geometry. She is a member of the French Academy of Sciences and holds the chair of algebraic geometry at the Collège de France.
John Colin Stillwell is an Australian mathematician on the faculties of the University of San Francisco and Monash University.
In mathematics, the Hilbert–Burch theorem describes the structure of some free resolutions of a quotient of a local or graded ring in the case that the quotient has projective dimension 2. Hilbert proved a version of this theorem for polynomial rings, and Burch proved a more general version. Several other authors later rediscovered and published variations of this theorem. Eisenbud gives a statement and proof.
In mathematics, the Demazure conjecture is a conjecture about representations of algebraic groups over the integers made by Demazure. The conjecture implies that many of the results of his paper can be extended from complex algebraic groups to algebraic groups over fields of other characteristics or over the integers. V. Lakshmibai, C. Musili, and C. S. Seshadri showed that Demazure's conjecture follows from their work on standard monomial theory, and Peter Littelmann extended this to all reductive algebraic groups.
Tsit Yuen Lam is a Hong Kong-American mathematician specializing in algebra, especially ring theory and quadratic forms.
Nolan Russell Wallach is a mathematician known for work in the representation theory of reductive algebraic groups. He is the author of the two-volume treatise Real Reductive Groups.
Irena Vassileva Peeva is a professor of mathematics at Cornell University, specializing in commutative algebra. She disproved the Eisenbud–Goto regularity conjecture jointly with Jason McCullough.
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.
Frank-Olaf Schreyer is a German mathematician, specializing in algebraic geometry and algorithmic algebraic geometry.
