Jeffry Ned Kahn is a professor of mathematics at Rutgers University notable for his work in combinatorics.
Jeffry Ned Kahn is a professor of mathematics at Rutgers University notable for his work in combinatorics.
Kahn received his Ph.D. from Ohio State University in 1979 after completing his dissertation under his advisor Dijen K. Ray-Chaudhuri. [1]
In 1980 he showed the importance of the bundle theorem for ovoidal Möbius planes. [2] In 1993, together with Gil Kalai, he disproved Borsuk's conjecture. [3] In 1996 he was awarded the Pólya Prize (SIAM).
He was an invited speaker at the 1994 International Congress of Mathematicians in Zurich.[ citation needed ]
In 2012, he was awarded the Fulkerson Prize (jointly with Anders Johansson and Van H. Vu) for determining the threshold of edge density above which a random graph can be covered by disjoint copies of a given smaller graph. [4] [5] Also in 2012, he became a fellow of the American Mathematical Society. [6]
The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing and hexagonal close packing arrangements. The density of these arrangements is around 74.05%.
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.
George Neil Robertson is a mathematician working mainly in topological graph theory, currently a distinguished professor emeritus at the Ohio State University.
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.
The Borsuk problem in geometry, for historical reasons incorrectly called Borsuk's conjecture, is a question in discrete geometry. It is named after Karol Borsuk.
In mathematical programming and polyhedral combinatorics, the Hirsch conjecture is the statement that the edge-vertex graph of an n-facet polytope in d-dimensional Euclidean space has diameter no more than n − d. That is, any two vertices of the polytope must be connected to each other by a path of length at most n − d. The conjecture was first put forth in a letter by Warren M. Hirsch to George B. Dantzig in 1957 and was motivated by the analysis of the simplex method in linear programming, as the diameter of a polytope provides a lower bound on the number of steps needed by the simplex method. The conjecture is now known to be false in general.
Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.
Gil Kalai is an Israeli mathematician and computer scientist. He is the Henry and Manya Noskwith Professor Emeritus of Mathematics at the Hebrew University of Jerusalem, Israel, Professor of Computer Science at the Interdisciplinary Center, Herzliya, and adjunct Professor of mathematics and of computer science at Yale University, United States.
Maria Chudnovsky is an Israeli-American mathematician working on graph theory and combinatorial optimization. She is a 2012 MacArthur Fellow.
Discrete & Computational Geometry is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986 by Jacob E. Goodman and Richard M. Pollack, the journal publishes articles on discrete geometry and computational geometry.
Van H. Vu is a Vietnamese mathematician and the Percey F. Smith Professor of Mathematics at Yale University.
Robin Thomas was a mathematician working in graph theory at the Georgia Institute of Technology.
In geometry, Kalai's 3d conjecture is a conjecture on the polyhedral combinatorics of centrally symmetric polytopes, made by Gil Kalai in 1989. It states that every d-dimensional centrally symmetric polytope has at least 3d nonempty faces.
Francisco (Paco) Santos Leal is a Spanish mathematician at the University of Cantabria, known for finding a counterexample to the Hirsch conjecture in polyhedral combinatorics. In 2015 he won the Fulkerson Prize for this research.
Karim Alexander Adiprasito is a German mathematician working at the University of Copenhagen and the Hebrew University of Jerusalem who works in combinatorics. He completed his PhD in 2013 at Free University Berlin under the supervision of Günter M. Ziegler. He has been a professor at the Hebrew University since 2015, and at the University of Copenhagen since 2019. He is of German and Indonesian descent, and bears an Indonesian surname.
The Kahn–Kalai conjecture, also known as the expectation threshold conjecture or more recently the Park-Pham Theorem, was a conjecture in the field of graph theory and statistical mechanics, proposed by Jeff Kahn and Gil Kalai in 2006. It was proven in a paper published in 2024.
Jinyoung Park is a South Korean mathematician at the Courant Institute of Mathematical Sciences at New York University working in combinatorics and graph theory. In 2022, she released a preprint, joint with Huy Tuan Pham, containing a proof of the Kahn–Kalai conjecture. Their paper was published in the Journal of the American Mathematical Society in 2024.
Read's conjecture is a conjecture, first made by Ronald Read, about the unimodality of the coefficients of chromatic polynomials in the context of graph theory. In 1974, S. G. Hoggar tightened this to the conjecture that the coefficients must be strongly log-concave. Hoggar's version of the conjecture is called the Read–Hoggar conjecture.
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