1.1. Number Theory
Programme leaders: H.W. Lenstra, R. Tijdeman
Description of the programme. Number theory studies the
properties of integers, with a historically strong emphasis on the study of
diophantine equations, that is, systems of equations that are to be solved in
integers. The methods of number theory are taken from several other branches
of mathematics. Traditionally, these include algebra and analysis, but in recent
times algebraic geometry has been playing a role of increasing importance as
well. It has also been discovered that number theory has important applications
in more applied areas, such as cryptography, dynamical systems theory and
numerical mathematics. These new developments stimulated the design,
analysis and use of algorithms, now called computational number theory. They led
to a unification rather than diversification of number theory. For example, the
applications in cryptography are strongly connected to algebraic geometry and
computational number theory; and algebraic number theory, which used to stand on
itself, is now pervading virtually all of number theory. Themes of the
programme reflect the mentioned research areas. They include finding points on
algebraic curves, applications of group theory and algebraic number theory, the
theory of finite fields, diophantine approximation, almost periodic and
recurrence sequences, primality tests and factorization methods, and the
development of efficient computer algorithms. Status of the
programme. The number theorists of the Stieltjes Institute made
important contributions to the current development and continue their
active participation. Their expertise and interests cover most of
present-day number theory. There is an excellent research climate for
number theory both within the Stieltjes Institute and at a national level, partly
as a result of the "groot project getaltheorie" of NWO/SWON, in which
the universities of Leiden, Amsterdam, Groningen, and Utrecht participate. The
very successful biweekly Number Theory Seminar, which is organized from within
the Stieltjes Institute, draws large audiences and serves as a meeting ground for
number theorists and as an introduction to research for graduate students. There
is a cooperation project between Leiden, CWI Amsterdam, and Groningen on the
factorization of integers. In addition there is a regular flow of visitors and
postdocs. In April 1999 there will be a workshop in number theory at
the Lorentz Centre in Leiden. Amsterdam will, in July 2000, be the venue of the
fourth Algorithmic Number Theory Symposium (ANTS), one of the major events
worldwide in computational number theory. On an international level,
there have always been close contacts between number theorists, through
correspondence, meetings, and personal visits. These have further intensified as
the result of the development of modern means of communication and the demise of
the Soviet empire. The number theorists in Stieltjes have close and long-standing
cooperations with mathematicians in virtually all countries where number theory
is done, including the United States, Canada, England, France, Germany, Italy,
Hungary, Poland, India, Japan and Australia. Research Staff (situation at January 1,2007) - Permanent
staff
- Dr. J. Brinkhuis (EUR) (from programme 4.1)
- Prof.dr. R.J.F. Cramer (UL/CWI)
- Dr. J.-H. Evertse (UL)
- Prof.dr. J.P. Hogendijk (UL/UU)
- Dr. C. Kraaikamp (TUD) (from programme 3.1)
- Prof.dr. H.W. Lenstra (UL)
- Dr. B. de Smit (UL)
- Prof.dr. P. Stevenhagen (UL)
- Dr. R.J. Stroeker (EUR)
- Prof.dr. R. Tijdeman (UL)
- Dr. R.W. van der Waall (UvA)
- Ph.D. students
- Drs. J. Bouw (UL)
- Drs. J. Brakenhoff (UL)
- Drs. J.L.A.H. Daems (UL)
- Drs W.H. Ekkelkamp (UL/CWI-NWO)
- Drs. R. de Haan (UL/CWI)
- Drs. B.J.H. Jansen (UL)
- Drs. W.J. Palenstijn (UL-NWO)
- Drs. S.W. Rosema (UL)
- Ir. I. Smeets (UL)
- Drs. T.C. Streng (UL)
- E.L. Toreao Dassen, MSc. (UL-EU)
- CWI participants
- Dr. S. Fehr
- Dr.ir. H.J.J. te Riele
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