Gil Kalai
Encyclopedia
Gil Kalai is the Henry and Manya Noskwith Professor of Mathematics
at the Hebrew University of Jerusalem
, and adjunct professor of mathematics and of computer science at Yale University
, and the editor of the Israel Journal of Mathematics.
. He was the recipient of the Pólya Prize
in 1992, the Erdős Prize
of the Israel Mathematical Society in 1993, and the Fulkerson Prize
in 1994. He is known for finding variants of the simplex algorithm
in linear programming
that can be proven to run in subexponential time, for showing that every monotone property of graphs
has a sharp phase transition
, for solving Borsuk's problem (known as Borsuk's conjecture
) on the number of pieces needed to partition convex sets into subsets of smaller diameter, and for his work on the Hirsch conjecture
on the diameter of convex polytope
s and in polyhedral combinatorics
more generally.
He was the winner of the 2012 Rothschild Prize in mathematics.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at the Hebrew University of Jerusalem
Hebrew University of Jerusalem
The Hebrew University of Jerusalem ; ; abbreviated HUJI) is Israel's second-oldest university, after the Technion – Israel Institute of Technology. The Hebrew University has three campuses in Jerusalem and one in Rehovot. The world's largest Jewish studies library is located on its Edmond J...
, and adjunct professor of mathematics and of computer science at Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
, and the editor of the Israel Journal of Mathematics.
Biography
Gil Kalai received his Ph.D. from Hebrew University in 1983, under the supervision of Micha Perles, and joined the Hebrew University faculty in 1985 after a postdoctoral fellowship at the Massachusetts Institute of TechnologyMassachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
. He was the recipient of the Pólya Prize
Pólya Prize (SIAM)
The Pólya Prize is a prize in mathematics, awarded by the Society for Industrial and Applied Mathematics. First given in 1969, the prize is named after Hungarian mathematician George Pólya...
in 1992, the Erdős Prize
Erdős Prize
- References :*...
of the Israel Mathematical Society in 1993, and the Fulkerson Prize
Fulkerson Prize
The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Programming Society and the American Mathematical Society . Up to three awards of $1500 each are presented at each International Symposium of the MPS...
in 1994. He is known for finding variants of the simplex algorithm
Simplex algorithm
In mathematical optimization, Dantzig's simplex algorithm is a popular algorithm for linear programming. The journal Computing in Science and Engineering listed it as one of the top 10 algorithms of the twentieth century....
in linear programming
Linear programming
Linear programming is a mathematical method for determining a way to achieve the best outcome in a given mathematical model for some list of requirements represented as linear relationships...
that can be proven to run in subexponential time, for showing that every monotone property of graphs
Hereditary property
In mathematics, a hereditary property is a property of an object, that inherits to all its subobjects, where the term subobject depends on the context. These properties are particularly considered in topology and graph theory.-In topology:...
has a sharp phase transition
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
, for solving Borsuk's problem (known as Borsuk's conjecture
Borsuk's conjecture
The Borsuk problem in geometry, for historical reasons incorrectly called a Borsuk conjecture, is a question in discrete geometry.-Problem:...
) on the number of pieces needed to partition convex sets into subsets of smaller diameter, and for his work on the Hirsch conjecture
Hirsch conjecture
In mathematical programming and polyhedral combinatorics, Hirsch's conjecture states 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...
on the diameter of convex polytope
Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn...
s and in polyhedral combinatorics
Polyhedral combinatorics
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....
more generally.
He was the winner of the 2012 Rothschild Prize in mathematics.
External links
- Kalai's home page at Hebrew University
- Combinatorics and more, Kalai's blog