Special Year on Gröbner Bases

March '97 - February '98

RISC-Linz, Hagenberg, Austria

The institute RISC-Linz of the Johannes Kepler Universität in Linz, Austria, will organize a Special Year on Gröbner Bases, from March 1997 until February 1998. The goals are

1. to interest and educate graduate students in the Gröbner bases method, which by now has become one of the standard methods in computer algebra,
2. to stimulate new research in this area by bringing together researchers in seminars and other events during the year,
3. to stimulate the interaction among researchers in computer algebra, commutative algebra, software design, and applications, as related to the theory of Gröbner bases.

The special year activities will be open to all graduate students and researchers working or having interest in the Gröbner bases method. We are working for partial support of a limited number of participants. Researchers on sabbatical and/or leave of absence are encouraged to get into contact with us.

Besides increased activities in seminars and colloquia, there will be two main activities during the Special Year on Gröbner Bases: an intensive course for graduate students taught by members of RISC-Linz and invited speakers, and a conference devoted to the theory and practice of Gröbner bases.

Intensive Course on Gröbner Bases

From January 12 until January 30, 1998, we will organize and teach an intensive course on Gröbner bases. The goal of this course is to provide a thorough introduction to Gröbner bases. Topics that will be relevant to this course include:

• abstract reduction relations and the properties of confluence and termination,
• term orderings for Gröbner bases and their classification,
• existence, uniqueness, and construction of Gröbner bases for polynomial ideals over a field,
• immediate applications to elimination theory, operations on ideals, and linear algebra in residue class rings,
• improved construction of Gröbner bases, such as criteria for eliminating unneccessary critical pairs, syzygies, and information on Hilbert functions,
• complexity analysis,
• more advanced applications to problems in algebraic geometry, such as Hilbert's Nullstellensatz, dimension of ideals, computation of radicals, primary decomposition of ideals,
• applications in computer aided geometric design, such as implicitization of algebraic curves and surfaces.

The course will be taught by Bruno Buchberger and Franz Winkler from RISC-Linz together with guest lecturers from other institutes (names will be announced soon). Participants in the course are expected to have a good basic understanding of algebra and some knowledge in computer programming.

International Conference on Gröbner Bases:
``33 Years of Gröbner Bases''

In February 2--4, 1998, RISC-Linz will organize a 3-day conference on Gröbner bases. A call for papers will be issued early next year. Franz Winkler will act as the chairman of the program committee. Topics of the conference include

• theoretical development of the theory of Gröbner bases,
• numerical aspects of the computation and use of Gröbner bases,
• applications of Gröbner bases in science and engineering,
• implementations and issues of software design in connection with Gröbner bases.

In addition to the regular program of the conference we plan to organize a software exhibition.

Accepted presentations at the conference will be published in a proceedings volume in ``Texts and Monographs in Symbolic Computation'', the RISC-Linz book series published by Springer-Verlag Wien New York.

The site of all events during the Special Year on Gröbner Bases will be the medieval Castle of Hagenberg, the home of RISC-Linz.

For additional information on the Special Year on Gröbner Bases please write to the organizers:

Bruno Buchberger Johannes Kepler Universität A-4040 Linz, Austria buchberger@risc.uni-linz.ac.at

Franz Winkler Johannes Kepler Universität A-4040 Linz, Austria winkler@risc.uni-linz.ac.at