Gröbner free methods and their applications
Barcelona, April 13-15 2026
Aula IC Facultat de Matemàtiques i Informàtica, University of Barcelona
This is a series of anual events following those organized in Bari 2025, and La Rioja 2024.
The goal of these meetings is to bring together researchers working on alternative methods for solving polynomial systems. While Gröbner bases have been highly influential, Buchberger’s algorithm can be computationally heavy when used by default. Gröbner-free approaches instead rely on linear algebra and combinatorics to obtain the same results more efficiently, reserving Gröbner basis computations for when they are truly needed.
Topics include but are not limited to
* Combinatorial methods for monomial and polynomial ideals
* Improvements and generalizations of Gröbner-related algorithms such as Janet’s and Macaulay’s.
* Algorithms for doing computations in subalgebras • 0-dimensional solving and bonding problems
* Applications in coding theory, cryptography, reverse engineering, biology, and algebraic statistics
As in the previous editions, our timing will be sufficiently relaxed to allow participants to discuss and work together.
Keynote Speakers
Gianira Alfarano, Université de Rennes
Skew-polynomial rings and algebraic coding theory
Cyclic codes are among the most extensively studied families of block codes in classical coding theory, as they provide the algebraic framework for the construction of important code families such as Reed–Solomon and BCH codes. A natural generalization of these codes is given by the so-called skew-cyclic codes. These codes are based on skew-polynomial rings in one indeterminate. The key difference from the commutative polynomial case is that, in the skew setting, the indeterminate does not commute with its coefficients. In this talk, we will discuss how the theory of skew-polynomial rings can be applied to algebraic coding theory. In particular, we will present some recent results concerning the minimum distance of skew-cyclic codes with respect to the Hamming, rank, and sum-rank metrics.
The presentation is based on the foundational work on skew-polynomial rings by Ore (1933) and by Lam and Leroy (1988–2012), as well as on the theory of skew-cyclic codes developed by Boucher, Ulmer, and collaborators (2007–2014), and on joint works with Lobillo, Neri, and Wachter-Zeh.
Roser Homs, Universitat Politècnica de Catalunya
Submission instructions and deadlines
If you are interested in giving a 30 minutes presentation, please submit an abstract (3 pages maximum) through Easychair.
The accepted abstracts will be distributed at the conference. Some of them, on decision of the Organizing Committee, will be allowed to submit a complete paper which will be published in a special issue of Journal AAECC, after a referee evaluation according to the standard of the Journal.
Deadline for submissions: February 28th 2026
Schedule (tentative)
Monday 13/04
09:00-09:30 Registration
09:30-10:30 Invited talk
10:30-11:00 Coffee Break
11:00-13:00 Contributed Talks
13:00-15:00 Lunch
15:00-18:00 Working Session
Tuesday 14/04
09:30-10:30 Invited talk
10:30-11:00 Coffee Break
11:00-13:00 Contributed Talks
13:00-15:00 Lunch
15:00-18:00 Working Session
20.30-22.00 Conference dinner
Wednesday 15/04
09:30-11:30 Contributed talks
11:30-12:00 Coffee Break
12:00-13:30 Contributed Talks
13:30-15:00 Lunch
15:00-18:00 Working Session
Registration
Registration is free, but we need participants to register by filling this form to make the proper arrangements.
Deadline for registration: March 15th 2026
Organizing Committee