Gröbner free methods and their applications

The influence of Gröbner bases on Algebra and Geometry during the last decades cannot be overstated; however, using Buchberger's algorithm as a default method in solving problems may lead to unnecessary computations.

Consequently, alternative algorithms have been proposed: Gröbner-free Solving (or, more generally, Degröbnerization) proposes to find alternative ways to get the same solutions, using, for example, tools from Linear Algebra and Combinatorics.

This approach consists in finding new ways to solve specific problems that have been originally solved using Gröbner basis computation and Buchberger's reduction, leaving the use of the latter only to the cases where it is really necessary; usually, the "new ways'' consist in using linear algebra and combinatorial methods.

Degröbnerization is also largely used to study the reverse problem with respect to solving, namely the bonding problem for algebras and ideals: Given the variety associated with a 0-dimensional ideal, i.e. a finite set of points, the structure of the quotient algebra (which actually contains more information than the ideal itself) can be recovered only using Combinatorics.

Four cornerstones of Degröbnerization are Auzinger-Stetter Matrices, Mourrain's notion of connected to 1, Lundqvist's fast algorithm for merging sorted lists of monomials and adding polynomials and Cerlienco-Mureddu Correspondence.

The aim of this conference is to bring together researchers on the main areas around Degröbnerization. We plan to have a conference, but also a workshop, with a timing sufficiently relaxed to allow participants to discuss and work together.