Related Research Articles
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.
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.
Amalie Emmy Noether was a German mathematician who made many important contributions to abstract algebra. She proved Noether's first and second theorems, 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 theories of rings, fields, and algebras. In physics, Noether's theorem explains the connection between symmetry and conservation laws.
In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and consequential conjectures about connections between number theory and geometry. Proposed by Robert Langlands, it seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. Widely seen as the single biggest project in modern mathematical research, the Langlands program has been described by Edward Frenkel as "a kind of grand unified theory of mathematics."
John Torrence Tate Jr. was an American mathematician distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry, and related areas in algebraic geometry. He was awarded the Abel Prize in 2010.
In algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings, as well as an array of properties that proved to be of interest both within the theory itself and for its applications, such as homological properties and polynomial identities.
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions, possibly in some generalized sense. A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which does not always equal ; or more generally an algebraic structure in which one of the principal binary operations is not commutative; one also allows additional structures, e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions.
Oscar Zariski was an American mathematician. The Russian-born scientist was one of the most influential algebraic geometers of the 20th century.
Richard Dagobert Brauer was a leading German and American mathematician. He worked mainly in abstract algebra, but made important contributions to number theory. He was the founder of modular representation theory.
Marshall Harvey Stone was an American mathematician who contributed to real analysis, functional analysis, topology and the study of Boolean algebras.
Michael Artin is an American mathematician and a professor emeritus in the Massachusetts Institute of Technology Mathematics Department, known for his contributions to algebraic geometry.
Jan Denef is a Belgian mathematician. He is an Emeritus Professor of Mathematics at the Katholieke Universiteit Leuven.
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations acting on their elements. 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 it from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. The abstract perspective on algebra has become so fundamental to advanced mathematics that it is simply called "algebra", while the term "abstract algebra" is seldom used except in pedagogy.
Maurice Auslander was an American mathematician who worked on commutative algebra, homological algebra and the representation theory of Artin algebras. He proved the Auslander–Buchsbaum theorem that regular local rings are factorial, the Auslander–Buchsbaum formula, and, in collaboration with Idun Reiten, introduced Auslander–Reiten theory and Auslander algebras.
In algebra, Auslander–Reiten theory studies the representation theory of Artinian rings using techniques such as Auslander–Reiten sequences and Auslander–Reiten quivers. Auslander–Reiten theory was introduced by Maurice Auslander and Idun Reiten and developed by them in several subsequent papers.
In mathematics, Lafforgue's theorem, due to Laurent Lafforgue, completes the Langlands program for general linear groups over algebraic function fields, by giving a correspondence between automorphic forms on these groups and representations of Galois groups.
Georgia McClure Benkart was an American mathematician who was known for her work in the structure and representation theory of Lie algebras and related algebraic structures. She published over 130 journal articles and co-authored three American Mathematical Society memoirs in four broad categories: modular Lie algebras; combinatorics of Lie algebra representations; graded algebras and superalgebras; and quantum groups and related structures.
Kiyoshi Igusa is a Japanese-American mathematician and a professor at Brandeis University. He works in representation theory and topology.
Andrei Vladimirovich Roiter was a Ukrainian mathematician, specializing in algebra.
Lyudmyla Oleksandrivna Nazarova is a Ukrainian mathematician specializing in linear algebra and representation theory.
References
- ↑ Birthdate from Library of Congress catalog entry, retrieved 2021-04-05
- ↑ "Gordana Todorov", People, Northeastern College of Science, retrieved 2021-04-05
- ↑ Gordana Todorov at the Mathematics Genealogy Project
- ↑ "Yoshie Igusa, 1927 – 2019", Baltimore Sun, 26 May 2019 – via Legacy.com
- ↑ Huard, François; Lanzilotta, Marcelo (2013), "Self-injective right Artinian rings and Igusa Todorov functions", Algebras and Representation Theory, 16 (3): 765–770, arXiv: 1101.1936 , doi:10.1007/s10468-011-9330-2, MR 3049670
- ↑ Wei, Jiaqun (2009), "Finitistic dimension and Igusa–Todorov algebras", Advances in Mathematics , 222 (6): 2215–2226, doi: 10.1016/j.aim.2009.07.008 , MR 2562782
- ↑ Coelho, Flávio Ulhoa (1990), "A generalization of Todorov's theorem on preprojective partitions", Communications in Algebra, 18 (5): 1401–1423, doi:10.1080/00927879008823972, MR 1059737
- ↑ Zhou, Panyue (2018), "A right triangulated version of Gentle-Todorov's theorem", Communications in Algebra, 46 (1): 82–89, doi:10.1080/00927872.2017.1310871, MR 3764845
