# The 50th Anniversary of Gröbner Bases

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*Takayuki Hibi*

A publication of the Mathematical Society of Japan

The discovery of the algorithm by Bruno Buchberger in July
1965, the so-called Buchberger algorithm used to compute Gröbner
bases of ideals of the polynomial ring, led to the birth of the
exciting research area in modern mathematics called computer
algebra.

The 8th Mathematical Society of Japan Seasonal Institute (MSJ SI
2015), entitled The 50th Anniversary of Gröbner Bases, was held
in July 2015. This volume contains the proceedings of MSJ SI 2015 and
consists of 14 papers related to computer algebra, algebraic
statistics, D-modules, convex polytopes, and toric ideals. These
papers enable readers to explore current trends in Gröbner bases.
Young researchers will find a treasury of fascinating
research problems which are pending. The foreword was contributed by
Bruno Buchberger and includes a secret story on the discovery of the
Buchberger algorithm.

Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS.

Volumes in this series are freely available electronically 5 years post-publication.

#### Readership

Graduate students and researchers interested in Gröbner bases.