This series of annual international conferences, Gröbner Free Methods and Their Applications, is devoted to exploring alternative approaches to solving polynomial systems beyond the classical Gröbner basis framework. The meetings bring together researchers from Algebra, Geometry, Combinatorics, and related fields to exchange ideas, develop new techniques, and foster collaborations in a relaxed and interactive setting.
Building on the success of previous editions, the series highlights both theoretical advances and applications, from algorithmic innovations to connections with coding theory, cryptography, and algebraic statistics.
Editions
Topics of the Conference
Gröbner bases have profoundly influenced Algebra and Geometry in recent decades. Yet, the systematic use of Buchberger’s algorithm as a default tool often leads to unnecessary computations. Degröbnerization or Gröbner-free solving seeks alternative strategies that achieve the same goals using Linear Algebra and Combinatorics, reserving Gröbner basis computations for cases where they are truly essential. Beyond solving, Degröbnerization also addresses the bonding problem for algebras and ideals: recovering the structure of the quotient algebra associated with a finite variety purely through combinatorial methods. Key concepts in this framework include Auzinger–Stetter matrices, Mourrain’s notion of “connected to 1”, Lundqvist’s fast algorithms, and the Cerlienco–Mureddu correspondence.
The conference welcomes contributions in, but not limited to, the following areas:
Combinatorial techniques for monomial and polynomial ideals
Advances in Hilbert’s program on the effective manipulation of polynomial ideals (resolutions, Hilbert functions, etc.)
Improvements and optimizations of Buchberger’s, Janet’s, and Macaulay’s algorithms
Extensions of these algorithms to broader classes of rings (including non-commutative)
Zero-dimensional solving and bonding problems
Gröbner and Gröbner-free methods for ideals generated by generic objects
Applications of classical matrices in the study of algebras and ideals
Degröbnerization beyond zero-dimensional ideals, including subalgebras and non-commutative settings
Tag-variable techniques
Parametric polynomial system solving
Applications in coding theory, cryptography, reverse engineering, biology, and algebraic statistics