Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
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.
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.
Singular is a computer algebra system for polynomial computations with special emphasis on the needs of commutative and non-commutative algebra, algebraic geometry, and singularity theory. Singular has been released under the terms of GNU General Public License. Problems in non-commutative algebra can be tackled with the Singular offspring Plural. Singular is developed under the direction of Wolfram Decker, Gert-Martin Greuel, Gerhard Pfister, and Hans Schönemann, who head Singular's core development team within the Department of Mathematics of the Technische Universität Kaiserslautern. In the DFG Priority Program 1489, interfaces to GAP, Polymake and Gfan are being developed in order to cover recently established areas of mathematics involving convex and algebraic geometry, such as toric and tropical geometry.
In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities and allowing "varieties" defined over any commutative ring.
In mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers – that is, for it to not be factorizable into the product of non-constant polynomials with rational coefficients.
David Bryant Mumford is an American mathematician known for his work in algebraic geometry and then for research into vision and pattern theory. He won the Fields Medal and was a MacArthur Fellow. In 2010 he was awarded the National Medal of Science. He is currently a University Professor Emeritus in the Division of Applied Mathematics at Brown University.
Michael Artin is a German-American mathematician and a professor emeritus in the Massachusetts Institute of Technology Mathematics Department, known for his contributions to algebraic geometry.
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.
David Eisenbud is an American mathematician. He is a professor of mathematics at the University of California, Berkeley and former director of the then Mathematical Sciences Research Institute (MSRI), now known as Simons Laufer Mathematical Sciences Institute (SLMath). He served as Director of MSRI from 1997 to 2007, and then again from 2013 to 2022.
Steven Mark Zucker was an American mathematician who introduced the Zucker conjecture, proved in different ways by Eduard Looijenga (1988) and by Leslie Saper and Mark Stern (1990).
Bernd Sturmfels is a Professor of Mathematics and Computer Science at the University of California, Berkeley and is a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 2017.
Barry Charles Mazur is an American mathematician and the Gerhard Gade University Professor at Harvard University. His contributions to mathematics include his contributions to Wiles's proof of Fermat's Last Theorem in number theory, Mazur's torsion theorem in arithmetic geometry, the Mazur swindle in geometric topology, and the Mazur manifold in differential topology.
Theodor Schönemann, also written Schoenemann, was a German mathematician who obtained several important results in number theory concerning the theory of congruences, which can be found in several publications in Crelle's journal, volumes 17 to 40. Notably, he obtained Hensel's lemma before Hensel, Scholz's reciprocity law before Scholz, and formulated Eisenstein's criterion before Eisenstein. He also studied, under the form of integer polynomials modulo both a prime number and an irreducible polynomial, what can nowadays be recognized as finite fields.
Eric Mark Friedlander is an American mathematician who is working in algebraic topology, algebraic geometry, algebraic K-theory and representation theory.
Haruzo Hida is a Japanese mathematician, known for his research in number theory, algebraic geometry, and modular forms.
Stephen S. Kudla is an American mathematician working in arithmetic geometry and automorphic forms. He is a professor in the Department of Mathematics at the University of Toronto.
Donal O'Shea is a Canadian mathematician, who is also noted for his bestselling books. He served as the fifth president of New College of Florida in Sarasota, from July 1, 2012, until June 30, 2021. He was succeeded by Patricia Okker on July 1, 2021. Before coming to New College, he served in various roles at Mount Holyoke College, including professor of mathematics, dean of faculty, and vice president for academic affairs.
Henry Koewing "Hal" Schenck is an American mathematician, known for his work in algebraic geometry and commutative algebra. He holds the Rosemary Kopel Brown Eminent Scholars Chair in mathematics at Auburn University.
