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

 Chair: Carlos D'Andrea

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 Oriol Reig: The Waring rank problem and algorithms

13:30-15:00 Lunch

15:00-18:00 Working Session: Gianira Alfarano

 Chair: Samuel Lundqvist

Goal: Construct optimal codes in the rank metric using skew polynomials.
Skew cyclic codes are a non-commutative generalization of classical cyclic codes, built using skew polynomials over a field extension. Their structure is determined by a defining set, which controls both the dimension and the rank distance of the code. In https://doi.org/10.1016/j.ffa.2020.101772, we have constructed Maximum Rank Distance (MRD) skew cyclic codes by choosing defining sets with a very regular structure (an arithmetic progression), which guarantees optimal rank distance. The question is whether one can construct MRD codes from more general defining sets, where this structure is less rigid but still sufficiently controlled. Such new constructions are known not to exist when the degree extension is prime, while in the general case the problem remains open.

Tuesday 14/04

 Chair: Fatemeh Mohammadi

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: Graphical models with toric vanishing ideals - Roser Homs

 Chair: Teo Mora

Goal: Find graphs (besides trees) such that the vanishing ideal of the corresponding graphical model is toric.
In the case of trees, linear non-Gaussian graphical models have toric vanishing ideals (ArXiv 2112.10875). In ArXiv 2105.13357, Misra and Sullivant provide criteria to construct graphs with Gaussian graphical models with toric vanishing ideals. We will start by studying small examples provided by Misra and Sullivant, use algebraic software to compute the vanishing ideal in the analogous non-Gaussian model and use tools to check toricity of such ideals.

20.00-22.00 Conference dinner: Restaurant Can Ros, Carrer d'Emília Llorca Martín, 7, in the Barceloneta neighbourhood.

Wednesday 15/04

 Chair: Michela Ceria

Contributed talks

10:00-10:30 Filip Jonsson Kling: The Gröbner basis for powers of a general linear form in a monomial complete intersection /span>

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 Emily Berghofer: Constructing Koszul Filtrations: Part 1

12:20-12:50 Lisa Nicklasson: Constructing Koszul filtrations: Part 2

13:00-15:00 Lunch

15:00-18:00 Working Session: Koszul filtrations for G-quadratic toric ideals - Lisa Nicklasson

 Chair: Per Bäck

Goal: Investigate a conjecture on Koszul filtrations of G-quadratic toric ideals posed in arXiv:2602.06490.
The conjecture states that any toric ideal with a quadratic Gröbner basis has a monomial Koszul filtration, a property which does indeed hold in the case of the DegRevLex term order. The idea for the workshop is to collect examples of toric ideals from the literature which has quadratic Gröbner bases w.r.t. other term orders, and test whether they satisfy the conjecture. Given that the answer is positive, what does the Koszul filtration look like? Further, we may explore the opposite direction: Given a monomial Koszul filtration, can we construct a quadratic Gröbner basis for the given toric ideal?