René Schoof (born 8 May 1955 in

Den Helder Den Helder () is a municipality and a city in the Netherlands, in the province of North Holland. Den Helder occupies the northernmost point of the North Holland peninsula. It is home to the country's main naval base. From here the Royal TESO fe ...

)R.J. Schoof, 1955 -
at the University of Amsterdam ''Album Academicum'' website is a mathematician from the Netherlands who works in

Algebraic Number Theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...

Arithmetic Algebraic Geometry In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties. ...

Computational Number Theory In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms ...

and Coding Theory. He received his PhD in 1985 from the University of Amsterdam with Hendrik Lenstra (''Elliptic Curves and Class Groups''). He is now a professor at the University Tor Vergata in Rome. In 1985, Schoof discovered an algorithm which enabled him to count points on elliptic curves over finite fields in

polynomial time In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by ...

.René Schoof: ''Elliptic curves over finite fields and the calculation of square roots mod p'', Mathematics of Computation, No. 44, 1985, 483–494. This was important for the use of elliptic curves in cryptography, and represented a theoretical breakthrough, as it was the first deterministic polynomial time algorithm for counting points on elliptic curves. The algorithms known before (e.g. the baby-step giant-step algorithm) were of exponential running time. His algorithm was improved by

A. O. L. Atkin Arthur Oliver Lonsdale Atkin (31 July 1925 – 28 December 2008), who published under the name A. O. L. Atkin, was a British mathematician. As an undergraduate during World War II, Atkin worked at Bletchley Park cracking German codes. He receiv ...

(1992) and Noam Elkies (1990). He obtained the best known result extending Deligne's Theorem for finite flat group schemes to the non commutative setting, over certain local Artinian rings. His interests range throughout Algebraic Number Theory, Arakelov theory, Iwasawa theory, problems related to existence and classification of Abelian varieties over the rationals with bad reduction in one prime only, and algorithms. In the past, René has also worked with

Rubik's cube The Rubik's Cube is a Three-dimensional space, 3-D combination puzzle originally invented in 1974 by Hungarians, Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik t ...

s by creating a common strategy in

speedsolving Speedcubing (also known as speedsolving, or cubing) is a competitive sport involving solving a variety of combination puzzles, the most famous being the 3x3x3 puzzle or Rubik's Cube, as quickly as possible. An individual who practices solving tw ...

used to set many world records known as F2L Pairs, in which the solver creates four 2-piece "pairs" with one edge and corner piece which are each "inserted" into F2L slots in the

CFOP The CFOP method (Cross – F2L – OLL – PLL), sometimes known as the Fridrich method, is one of the most commonly used methods in speedsolving a 3×3×3 Rubik's Cube. This method was first developed in the early 1980s combining innovations by ...

method to finish the first two layers of a 3x3x3 Rubik's cube. This strategy is also used for all cubes of higher order (4x4x4 and up) in the Reduction, Yau, and Hoya methods if CFOP is used for their 3x3x3 stages. He also wrote a book on Catalan's conjecture.

External links

Homepage

Some publications

* ''Counting points of elliptic curves over finite fields'', Journal des Théories des Nombres de Bordeaux, No. 7, 1995, 219–254
pdf
* With Gerard van der Geer, Ben Moonen (editors): ''Number fields and function fields – two parallel worlds'', Birkhäuser 2005 * ''Finite flat group schemes over Artin rings'', Compositio Mathematica, v. 128 (2001), 115 * ''Catalan's Conjecture'', Universitext, Springer, 2008

References

{{DEFAULTSORT:Schoof, Rene 1955 births Living people 20th-century Dutch mathematicians 21st-century Dutch mathematicians Number theorists University of Amsterdam alumni People from Den Helder University of Rome Tor Vergata faculty

See also

External links

Some publications

References