Nowadays, it is well-known that also long-standing open problems in Algebraic Geometry can benefit of algorithmic methods that are developed by Computer Algebra.

The first obvious reason is that algorithms allow the construction of examples, from which researchers can deduce possible solutions to the questions they deal with. In this context, the necessity to design new algorithms for specific topics of interest or to optimize the existing ones often arises.  Indeed, several existing algorithms theoretically allow some explicit computations (e.g. Groebner Bases) but in practice they do not give the desired result in a reasonable time, or using a reasonable amount of memory.

The second less obvious reason is that projecting an algorithm can give a new insight in the problem one is trying to solve. On the one hand, the algorithmic approach to a problem gives the chance to prove a statement in a constructive way; on the other hand, the effort needed to obtain a new Computer Algebra tool to tackle an open problem often allows to better enter the mechanism of the problem itself, highlighting new features that could not be seen with an existential approach.

As a consequence of the two above points, investigations in Algebraic Geometry from a computational point of view can also provide applications in other fields (e.g. coding theory, cryptography, computer graphics).

This session aims at gathering specialists from different areas (Algebraic Geometry, Computer Algebra, Applied Mathematics) and discuss interactions between them.

Talks should focus on

• algebraic and combinatorial aspects of problems in Algebraic Geometry;

• algorithms and constructive methods for Algebraic Geometry and applications;

• implementation of algorithms and optimization, possibly with comparisons with existing ones.

For the speakers and abstracts of the session held at ACA 2019 see  this webpage, and for those of the session at ACA 2021 this webpage

TALKS AND SPEAKERS

• On classification of algebraic curves and surfaces, using algorithmic methods, Meirav Amram (SCE, Israel) slides

• On the weighted proximity graph of the base locus of a plane Cremona map, Alberto Calabri (University of Ferrara, Italy) slides

• The m-ovoids of W(5, 2) and their generalizations, Michela Ceria (Politecnico di Bari, Italy) slides

• Jet schemes of Pfaffian ideals, Emanuela De Negri (University of Genova, Italy) slides

• Binary curves of genera four and five, Dušan Dragutinovic (Utrecht University, Netherlands) slides

• Free Resolutions and Generalized Hamming Weights of binary linear codes, Ignacio García-Marco (Universidad de La Laguna, Tenerife, Spain) slides 

• Irreducible Supernatural Bundles on Grassmannians, Ozhan Genc (Jagiellonian University, Krakow, Poland) slides

• Sumsets and the Castelnuovo-Mumford regularity of projective monomial curves, Mario Gonzalez-Sanchez (University of Valladolid, Spain) slides

• Degroebnerization for data modelling problems, Teo Mora (University of Genova, Italy) slides

• Generalizing Möller algorithm: a flexibility issue, Teo Mora (University of Genova, Italy) slides

• Infinite free resolutions induced by Pommaret-like bases over Clements–Lindström rings, Matthias Orth (University of Kassel, Germany) slides

• Applying Machine Learning to the Computation of Pommaret Bases— A Progress Report, Werner M. Seiler (University of Kassel, Germany) slides

• An algorithmic approach to characterize Cohen-Macaulay binomial edge ideals of small graphs, Francesco Strazzanti  (University of Genova, Italy) slides

ORGANIZERS
Cristina Bertone,  Dipartimento di Matematica "G.Peano", Università di Torino, Italy,  cristina.bertone@unito.it
Francesca Cioffi, Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Università di Napoli Federico II, Italy, cioffifr@unina.it