Related Research Articles
William Thomas TutteOC FRS FRSC was an English and Canadian codebreaker and mathematician. During the Second World War, he made a brilliant and fundamental advance in cryptanalysis of the Lorenz cipher, a major Nazi German cipher system which was used for top-secret communications within the Wehrmacht High Command. The high-level, strategic nature of the intelligence obtained from Tutte's crucial breakthrough, in the bulk decrypting of Lorenz-enciphered messages specifically, contributed greatly, and perhaps even decisively, to the defeat of Nazi Germany. He also had a number of significant mathematical accomplishments, including foundation work in the fields of graph theory and matroid theory.
In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid axiomatically, the most significant being in terms of: independent sets; bases or circuits; rank functions; closure operators; and closed sets or flats. In the language of partially ordered sets, a finite simple matroid is equivalent to a geometric lattice.
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at each (triennial) International Symposium of the MOS. Originally, the prizes were paid out of a memorial fund administered by the AMS that was established by friends of the late Delbert Ray Fulkerson to encourage mathematical excellence in the fields of research exemplified by his work. The prizes are now funded by an endowment administered by MPS.
Paul D. Seymour is a British mathematician known for his work in discrete mathematics, especially graph theory. He was responsible for important progress on regular matroids and totally unimodular matrices, the four colour theorem, linkless embeddings, graph minors and structure, the perfect graph conjecture, the Hadwiger conjecture, claw-free graphs, χ-boundedness, and the Erdős–Hajnal conjecture. Many of his recent papers are available from his website.
Jack R. Edmonds is an American-born and educated computer scientist and mathematician who lived and worked in Canada for much of his life. He has made fundamental contributions to the fields of combinatorial optimization, polyhedral combinatorics, discrete mathematics and the theory of computing. He was the recipient of the 1985 John von Neumann Theory Prize.
In mathematics, a regular matroid is a matroid that can be represented over all fields.
In graph theory, a branch-decomposition of an undirected graph G is a hierarchical clustering of the edges of G, represented by an unrooted binary tree T with the edges of G as its leaves. Removing any edge from T partitions the edges of G into two subgraphs, and the width of the decomposition is the maximum number of shared vertices of any pair of subgraphs formed in this way. The branchwidth of G is the minimum width of any branch-decomposition of G.
Uppaluri Siva Ramachandra Murty, or U. S. R. Murty, is a Professor Emeritus of the Department of Combinatorics and Optimization, University of Waterloo.
Michel Xavier Goemans is a Belgian-American professor of applied mathematics and the RSA Professor of Mathematics at MIT working in discrete mathematics and combinatorial optimization at CSAIL and MIT Operations Research Center.
James Anthony Dominic Welsh is an English mathematician and emeritus professor of Oxford University's Mathematical Institute. He is an expert in matroid theory, the computational complexity of combinatorial enumeration problems, percolation theory, and cryptography.
Alexander (Lex) Schrijver is a Dutch mathematician and computer scientist, a professor of discrete mathematics and optimization at the University of Amsterdam and a fellow at the Centrum Wiskunde & Informatica in Amsterdam. Since 1993 he has been co-editor in chief of the journal Combinatorica.
In the mathematical theory of matroids, a minor of a matroid M is another matroid N that is obtained from M by a sequence of restriction and contraction operations. Matroid minors are closely related to graph minors, and the restriction and contraction operations by which they are formed correspond to edge deletion and edge contraction operations in graphs. The theory of matroid minors leads to structural decompositions of matroids, and characterizations of matroid families by forbidden minors, analogous to the corresponding theory in graphs.
Rota's excluded minors conjecture is one of a number of conjectures made by mathematician Gian-Carlo Rota. It is considered to be an important problem by some members of the structural combinatorics community. Rota conjectured in 1971 that, for every finite field, the family of matroids that can be represented over that field has only finitely many excluded minors. A proof of the conjecture has been announced by Geelen, Gerards, and Whittle.
In the mathematical theory of matroids, a matroid representation is a family of vectors whose linear independence relation is the same as that of a given matroid. Matroid representations are analogous to group representations; both types of representation provide abstract algebraic structures with concrete descriptions in terms of linear algebra.
Balázs Szegedy is a Hungarian mathematician whose research concerns combinatorics and graph theory.
Gérard Pierre Cornuéjols is the IBM University Professor of Operations Research in the Carnegie Mellon University Tepper School of Business. His research interests include facility location, integer programming, balanced matrices, and perfect graphs.
Martin Grötschel is a German mathematician known for his research on combinatorial optimization, polyhedral combinatorics, and operations research. From 1991 to 2012 he was Vice President of the Zuse Institute Berlin (ZIB) and served from 2012 to 2015 as ZIB's President. From 2015 to 2020 he was President of the Berlin-Brandenburg Academy of Sciences and Humanities (BBAW).
Collette René Coullard is an American mathematician, industrial engineer, operations researcher, and matroid theorist known for her research on combinatorial optimization problems that combine facility location and stock management. Formerly a professor at Purdue University, the University of Waterloo, Northwestern University, and Lake Superior State University, she has retired to become a professor emeritus.
Henry Howland Crapo was an American-Canadian mathematician who worked in algebraic combinatorics. Over the course of his career, he held positions at several universities and research institutes in Canada and France. He is noted for his work in matroid theory and lattice theory.
References
- ↑ Jim Geelen at the Canada Research Chairs website.
- ↑ 2003 Fulkerson Prize citation, retrieved 2012-08-18.
- ↑ Geelen, J. F.; Gerards, A. M. H.; Kapoor, A. (2000), "The Excluded Minors for GF(4)-Representable Matroids", Journal of Combinatorial Theory , Series B, 79 (2): 247–299, doi: 10.1006/jctb.2000.1963
- ↑ Winners of the Coxeter–James Prize.
- ↑ Jim Geelen at the Mathematics Genealogy Project.
- ↑ "2006 Coxeter James Prize" (PDF).
| International | |
|---|---|
| National | |
| Academics | |
   | This article about a Canadian scientist is a stub. You can help Wikipedia by expanding it. |
 | This article about a mathematician is a stub. You can help Wikipedia by expanding it. |