Nowadays, it is well-known that also long-standing open problems in Algebraic Geometry can benefit from 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 points above, investigations in Algebraic Geometry from a computational point of view can also provide applications in other fields (e.g. coding theory, cryptography, computer graphics, data clouds, algebraic statistics).

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.

See the speakers and abstracts of the session held at ACA 2019 at this webpage

SCHEDULE AND ZOOM LINK
The talks will be on July 23 (Friday), 25 (Sunday), and 26 (Monday) between 15 and 18.30 CEST.
Here you find the schedule of the session. The interested attendees should write to both organizers to get the zoom link.

TALKS AND SPEAKERS

• Simplification of λ-ring expressions in the Grothendieck ring of Chow motives, David Alfaya (Comillas Pontifical University, Madrid, Spain)

• Fundamental groups in classification of algebraic surfaces, Meirav Amram (Shamoon College of Engineering, Israel)

• Waring decompositions of real binary forms and Brion’s formula, Macarena Ansola Fernández-Enríquez (Universidad Complutense de Madrid, Spain)

• How to cover rational surfaces with few rational parametrization images, Jorge Caravantes (Universidad de Alcala, Spain)

• Secret sharing schemes from hypersurfaces over finite fields, Michela Ceria (Politecnico di Bari, Italy)

• A characteristic free approach to secant varieties of triple Segre products, Emanuela De Negri (Università di Genova, Italy)

• A practical method to compute the geometric Picard lattice of K3 surfaces of degree 2, Dino Festi (Università di Milano, Italy)

• Gluing semigroup rings and the Cohen-Macaulay property, Philippe Gimenez (University of Valladolid, Spain)

• The Gröbner fan of the Hilbert scheme, Paolo Lella (Politecnico di Milano, Italy)

• De Nugis Groebnerialium 6: Rump, Ufnarovski,Zacharias, Ferdinando Mora (Università di Genova, Italy)

• Why you should never think of using Gröbner basis in Algebraic Statistics, Theo Moriarty (Italy)

• Cotangent spaces and separated re-embeddings, Le Ngoc Long (Universität Passau, Germany)

• Computational VGIT for Complete Intersections and an Hyperplane, Theodoros Papazachariou (University of Essex, UK)

• Relative Gröbner and Involutive Bases for Ideals in Quotient Rings, Matthias Orth (Universität Kassel, Germany)

• Finite quotients of surface braid groups and double Kodaira fibrations: an algorithmic approach, Francesco Polizzi (Università della Calabria, Italy)

• Poincaré polynomials for some Schubert varieties, Carmine Sessa (Università di Napoli Federico II, Italy)

• Hyperplane arrangements and k-Lefschetz properties, Michele Torielli (Hokkaido University, Japan)

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

SPONSOR
This session is partially funded by Dipartimento di Matematica "Giuseppe Peano", Università di Torino (Italy).