Amitai Regev (born December 7, 1940) is an Israeli mathematician, known for his work in ring theory.
He is the Herman P. Taubman Professor of Mathematics at the Weizmann Institute of Science. He received his doctorate from the Hebrew University of Jerusalem in 1972, under the direction of Shimshon Amitsur.
Regev has made significant contributions to the theory of polynomial identity rings (PI rings). In particular, he proved Regev's theorem that the tensor product of two PI rings is again a PI ring. [1] He developed so-called "Regev theory" that connects PI rings to representations of the symmetric group, and hence to Young tableaux. He has made seminal contributions to the asymptotic enumeration of Young tableaux and tableaux of hook shape, and together with William Beckner proved the Macdonald-Selberg conjecture for the infinite Lie algebras of type B, C, and D.
Amalie Emmy Noether was a German mathematician who made many important contributions to abstract algebra. She discovered Noether's First and Second Theorem, which are fundamental in mathematical physics. She was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl and Norbert Wiener as the most important woman in the history of mathematics. As one of the leading mathematicians of her time, she developed some theories of rings, fields, and algebras. In physics, Noether's theorem explains the connection between symmetry and conservation laws.
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers and additive number theory.
In functional analysis, a discipline within mathematics, given a C*-algebra A, the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic *-representations of A and certain linear functionals on A. The correspondence is shown by an explicit construction of the *-representation from the state. It is named for Israel Gelfand, Mark Naimark, and Irving Segal.
Daniel Gray "Dan" Quillen was an American mathematician. He is known for being the "prime architect" of higher algebraic K-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 1978.
Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called K-groups. These are groups in the sense of abstract algebra. They contain detailed information about the original object but are notoriously difficult to compute; for example, an important outstanding problem is to compute the K-groups of the integers.
In mathematics, a Young tableau is a combinatorial object useful in representation theory and Schubert calculus. It provides a convenient way to describe the group representations of the symmetric and general linear groups and to study their properties. Young tableaux were introduced by Alfred Young, a mathematician at Cambridge University, in 1900. They were then applied to the study of the symmetric group by Georg Frobenius in 1903. Their theory was further developed by many mathematicians, including Percy MacMahon, W. V. D. Hodge, G. de B. Robinson, Gian-Carlo Rota, Alain Lascoux, Marcel-Paul Schützenberger and Richard P. Stanley.
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.
Doron Zeilberger is an Israeli mathematician, known for his work in combinatorics.
In mathematics, the Robinson–Schensted correspondence is a bijective correspondence between permutations and pairs of standard Young tableaux of the same shape. It has various descriptions, all of which are of algorithmic nature, it has many remarkable properties, and it has applications in combinatorics and other areas such as representation theory. The correspondence has been generalized in numerous ways, notably by Knuth to what is known as the Robinson–Schensted–Knuth correspondence, and a further generalization to pictures by Zelevinsky.
Elliott Hershel Lieb is an American mathematical physicist and professor of mathematics and physics at Princeton University who specializes in statistical mechanics, condensed matter theory, and functional analysis.
Irving Kaplansky was a mathematician, college professor, author, and amateur musician.
In mathematics, the Littelmann path model is a combinatorial device due to Peter Littelmann for computing multiplicities without overcounting in the representation theory of symmetrisable Kac–Moody algebras. Its most important application is to complex semisimple Lie algebras or equivalently compact semisimple Lie groups, the case described in this article. Multiplicities in irreducible representations, tensor products and branching rules can be calculated using a coloured directed graph, with labels given by the simple roots of the Lie algebra.
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term abstract algebra was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning.
Shimshon Avraham Amitsur was an Israeli mathematician. He is best known for his work in ring theory, in particular PI rings, an area of abstract algebra.
In algebra, the Amitsur–Levitzki theorem states that the algebra of n × n matrices over a commutative ring satisfies a certain identity of degree 2n. It was proved by Amitsur and Levitsky (1950). In particular matrix rings are polynomial identity rings such that the smallest identity they satisfy has degree exactly 2n.
In mathematics, Plancherel measure is a measure defined on the set of irreducible unitary representations of a locally compact group , that describes how the regular representation breaks up into irreducible unitary representations. In some cases the term Plancherel measure is applied specifically in the context of the group being the finite symmetric group – see below. It is named after the Swiss mathematician Michel Plancherel for his work in representation theory.
In abstract algebra, Regev's theorem, proved by Amitai Regev, states that the tensor product of two PI algebras is a PI algebra.
Michel Louis Balinski was an applied mathematician, economist, operations research analyst and political scientist. As a Polish-American, educated in the United States, he lived and worked primarily in the United States and France. He was known for his work in optimisation, convex polyhedra, stable matching, and the theory and practice of electoral systems, jury decision, and social choice. He was Directeur de Recherche de classe exceptionnelle (emeritus) of the C.N.R.S. at the École Polytechnique (Paris). He was awarded the John von Neumann Theory Prize by INFORMS in 2013.
Oded Regev is an Israeli-American theoretical computer scientist and mathematician. He is a professor of computer science at the Courant institute at New York University. He is best known for his work in lattice-based cryptography, and in particular for introducing the learning with errors problem.
Aldridge Knight Bousfield, known as "Pete", was an American mathematician working in algebraic topology, known for the concept of Bousfield localization.