SPECIAL SESSION at the 26TH International Conference on Applications of Computer Algebra (ACA2021)
July 23-27, 2021, Virtual, Online
Hilbert's and Gordan's proofs of the Basissatz, which both consisted in giving an algorithm (an algorithm, not a procedure!) for producing a Groebner basis of a given ideal, settled the elementary approach toward Buchberger Theory: from the need of a term-ordering (stated implicitly by Hilbert and explicitly by Gordan) to the introduction of a rewriting procedure, which in Gordan is exactly Buchberger's.
The first group of researchers who deeply studied the notions and the tools introduced by Hilbert in his seminal paper, as Macaulay, Gunther and (mainly) Janet (who, studying with and under Hilbert, reinterpreted Riquier's results) are, consequently, the first which introduced the most important alternatives to Buchberger Algorithm for producing Groebner bases: Macaulay's Matrix from which Faugère's F4-F5 stemmed and Janet's involutive bases.
Recent research oriented itself toward the following three lines of investigation, which also represent the main focus of the talks expected for this section:
to improve and optimize Buchberger's, Janet's and Macaulay's algorithms;
to extend them to a wider class of (not necessarily commutative) rings; for instance Moeller's reformulation of Buchberger completion/test in terms of his Lifting Theorem is today available in each effectively given ring (in the sense used by Grete Hermann and van der Waerden);
to applications, for example in coding theory, cryptography, reverse engineering, algebraic statistics and so on.
Call for abstracts: if you are interested in participating to this session, please send to the organizers an abstract (2-3 pages, both in .tex and .pdf) by the 31st of May, using the template available here.
Talks and speakers:
Delphine Boucher (Université de Rennes 1) About Skew Reed-Solomon Codes Slides
Alessio Caminata (Università degli Studi di Genova) The complexity of Weil descent polynomial systems Slides
Steven Dougherty (University of Scranton) The use of Ideals in Algebraic Coding Theory
William Fajardo (Universidad Nacional de Colombia) The Maple library SPBWE.lib for working computationally with skew PBW extensions Slides
Amir Hashemi (Isfahan University of Technology, Institute for Research in Fundamental Sciences) Recursive Structures in Involutive Bases Theory Slides
Pavel Kolesnikov (Sobolev Institute of Mathematics) Standard bases method for vertex algebras Slides
F. J. Lobillo (Universidad de Granada) Minimum distance bounds on cyclic-skew-cyclic codes Slides
Hana Melánová (University of Vienna) Recovery from Power Sums Slides
Simone Naldi (Université de Limoges) On the computation of syzygies via multivariate matrix multiplication Slides
Vincent Neiger (Université de Limoges) Computing syzygies in finite dimension using fast linear algebra Slides
Patrick Solé (CNRS, Marseille) Type IV Codes over non unitary rings Slides
Victor Ufnarovski (Lunds University) Subalgebras in K[x] of small codimension Slides
Tristan Vaccon (Université de Limoges) On Gröbner bases over Tate Algebras Slides
AAECC Call for papers.
We kindly invite all participants to ACA 2021 to submit a paper to the special issue of the Journal
Applicable Algebra in Engineering, Communication and Computing (AAECC) dedicated to ACA 2021.
See the complete call for papers here.
Important dates
-Submission deadline: October 31, 2021
-Author notification: March 31, 2022
-Revisions due: April 30, 2022
-Publication in AAECC:
--Online : 2022
--Hardcopy: early 2023
ORGANIZERS
Michela Ceria
Department of Computer Science - Università degli Studi di Milano - michela.ceria@gmail.com
André Leroy
Faculté Jean Perrin à Lens - Université d’Artois - andre.leroy@univ-artois.fr
Teo Mora
Department of Mathematics - University of Genoa - 5919@unige.it