Gröbner free methods and their applications
Barcelona, April 13-15 2026
Aula IC Facultat de Matemàtiques i Informàtica, University of Barcelona
Gran Via 585, 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.
Information about lodging in Barcelona can be found here.
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
Markov basis and graphical models
A graphical model is a collection of probability distributions where the nodes of a graph represent random variables and the edges encode their statistical dependencies. In algebraic statistics, we are interested in the polynomial equations defining these models to facilitate parameter identifiability, model selection, or causal discovery. From an algebraic perspective, these models are semialgebraic sets. Given a parametrization, the objective is to find the vanishing ideal of the model's Zariski closure.
If the parametrization is monomial, the corresponding toric ideal is generated by a set of binomials known as a Markov basis. Originally developed by Diaconis and Sturmfels for conditional sampling, a Markov basis consists of binomial "moves" that allow for connectivity within a fiber. In this talk, we introduce Markov bases, discuss their relationship to Gröbner bases, and explore their interpretation as combinatorial moves. We will demonstrate how to prove that a generating set is a Markov basis using tableau representations for linear non-Gaussian graphical models whose underlying graphs are trees. This is joint work with Carlos Améndola, Mathias Drton, Alexandros Grosdos, and Elina Robeva.
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
Monday 13/04
09:00-09:30 Registration
09:30-10:30 Invited talk: Gianira Alfarano
10:30-11:00 Coffee Break
Contributed Talks
11:00-11:30 Matías Bender: Solving bihomogeneous polynomial systems with a zero-dimensional projection
11:40-12:10 Carles Checa: An effective criterion for multiple positive solutions of vertically parametrized polynomial systems
12:20-12:50 Sofia Bovero: Homogeneous Border Bases on infinite order ideals
13:00-13:30 Sami Barhoumi: On the Computation of Grobner Bases in Laurent Polynomial Rings
13:30-15:00 Lunch
15:00-18:00 Working Session: Gianira Alfarano
Tuesday 14/04
09:30-10:30 Invited talk: Roser Homs
10:30-11:00 Coffee Break
Contributed Talks
11:00-11:30 Francesca Cioffi: Counting finite O-sequences of a given multiplicity and experimental estimations of their growth
11:40-12:10 Danai Deligeorgaki: Combinatorial and algebraic perspectives on the marginal independence structure of Bayesian networks
12:20-12:50 Matthias Orth: Generalized Catalan numbers and Groebner bases
13:00-13:30 Victor Ufnarovski: Generic and almost monomial subalgebras
13:30-15:00 Lunch
15:00-18:00 Working Session: Roser Homs
20.00-22.00 Conference dinner
Wednesday 15/04
Contributed talks
10:00-10:30 Filip Jonsson Kling: The Gröbner basis for powers of a general linear form in a monomial complete intersection
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10:40-11:10 Barbara Betti: Eigenvalue and Homotopy Algorithms Using Khovanskii Bases
11:10-11:40 Coffee Break
Contributed talks
11:40-12:10 Oriol Reig: The Waring rank problem and algorithms
12:20-12:50 Emily Berghofer: Constructing Koszul Filtrations: Part 1
13:00-13:30 Lisa Nicklasson: Constructing Koszul filtrations: Part 2
13:30-15:00 Lunch
15:00-18:00 Working Session: Lisa Nicklasson
Registration
Registration is free, but we need participants to register by filling this form to make the proper arrangements.
Deadline for registration: March 23rd 2026
Organizing Committee