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The 50th anniversary of Gröbner bases. Proceedings of the 8th Mathematical Society of Japan-Seasonal Institute (MSJ-SI 2015), Osaka, Japan, July 1–10, 2015. (English) Zbl 1404.13003
Advanced Studies in Pure Mathematics 77. Tokyo: Mathematical Society of Japan (MSJ) (ISBN 978-4-86497-052-5/hbk). 436 p. (2018).

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Publisher’s description: The discovery of the algorithm by Bruno Buchberger on July 1965, so-called the Buchberger algorithm, to compute Gröbner bases of ideals of the polynomial ring had led the birth of the exciting research area called “Computer Algebra” in the modern mathematics. The 8th Mathematical Society of Japan Seasonal Institute (MSJ SI 2015) entitled “The 50th Anniversary of Gröbner Bases” was held on July 2015, which is the 50th year following the discovery of the Buchberger algorithm. This volume is the proceedings of MSJ SI 2015 and consists of 14 papers related with computer algebra, algebraic statistics, \(D\)-modules, convex polytopes and toric ideals. These papers enable the reader to look over the current trends on Gröbner bases. Especially, young researchers can reach a treasury of fascinating research problems which are pending. Foreword was contributed by Bruno Buchberger, where a secret story on the discovery of the Buchberger algorithm is stated.
The articles of this volume will be reviewed individually. For the preceding conference see [Zbl 1380.20002].
Indexed articles:
Abbott, John; Bigatti, Anna Maria, Gröbner bases for everyone with CoCoA-5 and CoCoALib, 1-24 [Zbl 1411.13001]
Buchberger, Bruno, Gröbner bases computation by triangularizing Macaulay matrices, 25-33 [Zbl 1458.13029]
Drton, Mathias, Algebraic problems in structural equation modeling, 35-86 [Zbl 1411.62128]
Fassino, Claudia; Möller, Hans Michael; Riccomagno, Eva, BM algorithms for noisy data and implicit regression modeling, 87-107 [Zbl 1411.13040]
Gross, Elizabeth; Petrović, Sonja; Richards, Donald; Stasi, Despina, The multiple roots phenomenon in maximum likelihood estimation for factor analysis, 109-119 [Zbl 1411.62058]
Higashitani, Akihiro; Kimura, Kyouko, A necessary condition for an edge ring to satisfy Serre’s condition (\(S_2\)), 121-128 [Zbl 1411.13034]
Hillar, Christopher J.; Krone, Robert; Leykin, Anton, Equivariant Gröbner bases, 129-154 [Zbl 1411.13029]
Kohl, Florian; Li, Yanxi; Rauh, Johannes; Yoshida, Ruriko, Semigroups – a computational approach, 155-170 [Zbl 1437.11166]
Meshkat, Nicolette; Rosen, Zvi; Sullivant, Seth, Algebraic tools for the analysis of state space models, 171-205 [Zbl 1411.13039]
Michałek, Mateusz, Selected topics on toric varieties, 207-252 [Zbl 1411.14057]
Oaku, Toshinori, Algorithms for \(D\)-modules, integration, and generalized functions with applications to statistics, 253-352 [Zbl 1411.13037]
Oaku, Toshinori, Localization, local cohomology, and the \(b\)-function of a \(D\)-module with respect to a polynomial, 353-398 [Zbl 1411.14023]
Trung, Tran Nam, A characterization of Gorenstein planar graphs, 399-409 [Zbl 1411.13028]
Vidunas, Raimundas; Takemura, Akimichi, Differential relations for the largest root distribution of complex non-central Wishart matrices, 411-436 [Zbl 1411.60025]
MSC:
13-06 Proceedings, conferences, collections, etc. pertaining to commutative algebra
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
14-06 Proceedings, conferences, collections, etc. pertaining to algebraic geometry
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
13D45 Local cohomology and commutative rings
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
00B25 Proceedings of conferences of miscellaneous specific interest
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