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 the designing of an algorithm can give a new insight in the problem one is trying to solve, giving in particular the chance to prove a statement in a constructive way, but also 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, data clouds).
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.
TALKS AND SPEAKERS
On algebraic and geometric properties of almost revlex ideals, Cristina Bertone (Università di Torino, Italy) slides
Some new elementary components of the Hilbert scheme of points, Mark Huibregtse (Skidmore College, USA) slides
New heuristics and extensions of the Dixon resultant for solving polynomial systems, Robert H. Lewis (Fordham University, USA) slides
Modular methods for rich algebraic geometry results on hyperplane arrangements, Elisa Palezzato (Hokkaido University, Japan) slides
Rational reparametrization of polynomial ODEs, PDEs and linear systems with radical coefficients, David Sevilla (University of Extremadura, Spain) slides
Algorithms for Polynomials in Legendre-Sobolev Bases, Stephen M. Watt (University of Waterloo, Canada) slides
Computing the genus of plane curves with cubic complexity in the degree, Martin Weimann (University of French Polynesia, French Polynesia) slides
The schedule of the conference is now available HERE
Cristina Bertone (firstname.lastname@example.org) Dipartimento di Matematica "G. Peano", Università di Torino, Italy
Francesca Cioffi (email@example.com) Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Università di Napoli Federico II, Italy