From the end of the 19th century to most of the 20th century several mathematicians made a conscious effort to avoid constructive arguments, emphasizing existential methods instead. The final decades of the 20th century witnessed a return to a constructive approach.

In this context, Computer Algebra grew up as a branch of mathematics and computer science that focuses on the development and implementation of algorithms and software systems to perform symbolic mathematical computations, also with a promotion of interactions with different topics, such as Algebraic Geometry and Commutative Algebra.

The first obvious reason of this interplay 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.

This synergy creates a virtuous cycle, where the development of Computer Algebra systems drives new mathematical discoveries, which in turn inspire further innovations in algorithm design. This session focuses on investigations in Algebraic Geometry from a computational point of view and on possible consequent applications in other fields (e.g. coding theory, cryptography, computer graphics). Hence, it aims at gathering specialists from different areas (Algebraic Geometry, Commutative Algebra, Computer Algebra, Applied Mathematics) and discuss interactions between them. 

Expected topics of presentations include (but are not limited to):

• 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.

TALKS AND SPEAKERS 

• Computational Classification and Generation of Algebraic Surfaces and Curves via Algorithms, Meirav Amram (SCE, Israel)

• On the shape of Betti diagrams of edge ideals, Sara Asensio (University of Valladolid, Spain)

• Khovanskii bases in computer algebra, Barbara Betti (Max Planck Institute, Leipzig, Germany)

• Solving parametric polynomial systems using generic Rational Univariate Representation, Florent Corniquel (IMJ-PRG and INRIA Paris, France)

• Homogenous Instanton Bundles on Grassmannians, Özhan Genç (Jagiellonian University, Poland)

• Computational Generation of Zariski Pairs in Conic-Line Arrangements, Gal Goren (Technion Institute of Technology Haifa, Israel)

• Geometric Foundations for Transformer in Gröbner Basis Computation, Yota Maeda (TU Darmstadt, Germany)

• Gröbner bases native to finitely generated commutative algebras with term order, with application to the Hodge algebra of minors, Abhiram Natarajan (University of Warwick, UK)

• Combinatorics of Schubert Cells in Random Network Coding, Alessandro Neri (Università Federico II Napoli, Italy)

• The Gröbner basis for powers of a general linear form in a monomial complete intersection, Matthias Orth (KU Leuven, Belgium)

• The moduli space of rational elliptic surfaces, Simone Pesatori (Università di Roma Tre, Italy)

• A computer-aided construction of non-homeomorphic double Kodaira fibrations that possess the same biregular invariants, Pietro Sabatino (ICAR-CNR, Italy)

• Constructing nonspecial divisors in the moduli space of cubic fourfolds, Elena Sammarco (Università di Roma Tre, Italy)

• Deterministic Determination of Axial Constants and Sectional Regularities, Werner M. Seiler (University of Kassel, Germany)

• Improving convex-dense bivariate factorization, Martin Weimann (Université Caen Normandie, France)

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