Gordana Todorov

Last updated

Gordana Todorov (born July 24, 1949) [1] is a mathematician interested in noncommutative algebra, representation theory, Artin algebra, and cluster algebra. She is a professor of mathematics at Northeastern University. [2]

Contents

Biography

Todorov earned her Ph.D. in 1978, at Brandeis University. Her dissertation, Almost Split Sequences in the Representation Theory of Certain Classes of Artin Algebras, was supervised by Maurice Auslander. [3]

Todorov is married to mathematician Kiyoshi Igusa, [4] with whom she is a frequent co-author. [5] The Igusa–Todorov functions [6] and Igusa–Todorov endomorphism algebras [7] are named for their joint work. Todorov is also the namesake of Todorov's theorem on preprojective partitions, [8] and the Gentle–Todorov theorem on abelian categories. [9]

Related Research Articles

André Weil 20th-century French mathematician

André Weil was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was a founding member and the de facto early leader of the mathematical Bourbaki group. The philosopher Simone Weil was his sister. The writer Sylvie Weil is his daughter.

Robert Langlands

Robert Phelan Langlands, is an American-Canadian mathematician. He is best known as the founder of the Langlands program, a vast web of conjectures and results connecting representation theory and automorphic forms to the study of Galois groups in number theory, for which he received the 2018 Abel Prize. He is an emeritus professor and occupies Albert Einstein's office at the Institute for Advanced Study in Princeton.

Teiji Takagi

Teiji Takagi was a Japanese mathematician, best known for proving the Takagi existence theorem in class field theory. The Blancmange curve, the graph of a nowhere-differentiable but uniformly continuous function, is also called the Takagi curve after his work on it.

John Tate American mathematician

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.

Ring theory Branch of algebra

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. 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.

Raoul Bott Hungarian-American mathematician

Raoul Bott was a Hungarian-American mathematician known for numerous basic 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.

Oscar Zariski American mathematician

Oscar Zariski was a Russian-born American mathematician and one of the most influential algebraic geometers of the 20th century.

Richard Brauer German-American mathematician

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.

Michael Artin American mathematician

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.

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.

Jan Denef Belgian mathematician

Jan Denef is a Belgian mathematician. He is an Emeritus Professor of Mathematics at the Katholieke Universiteit Leuven.

Maurice Auslander was an American mathematician who worked on commutative algebra and homological algebra. He proved the Auslander–Buchsbaum theorem that regular local rings are factorial, the Auslander–Buchsbaum formula, and 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 (1975) and developed by them in several subsequent papers.

In mathematics, the Auslander algebra of an algebra A is the endomorphism ring of the sum of the indecomposable modules of A. It was introduced by Auslander (1974).

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.

Jun-ichi Igusa was a Japanese mathematician who for over three decades was on the faculty at Johns Hopkins University. He is known for his contributions to algebraic geometry and number theory. The Igusa zeta-function, the Igusa quartic, Igusa subgroups, Igusa curves, and Igusa varieties are named after him.

Prakash Belkale is an Indian-American mathematician, specializing in algebraic geometry and representation theory.

Kiyoshi Igusa is a Japanese-American mathematician and a professor at Brandeis University. He works in representation theory and topology.

References

  1. Birthdate from Library of Congress catalog entry, retrieved 2021-04-05
  2. "Gordana Todorov", People, Northeastern College of Science, retrieved 2021-04-05
  3. Gordana Todorov at the Mathematics Genealogy Project
  4. "Yoshie Igusa, 1927 – 2019", Baltimore Sun, 26 May 2019 via Legacy.com
  5. Igusa, Kiyoshi (August 2019), 40 years of collaboration with Gordana (PDF)
  6. 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
  7. 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
  8. 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
  9. 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