SS9 - Algebraic geometry from an algorithmic point of view
link to the session's webpage
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.
Session organizers
| Cristina Bertone (Dipartimento di Matematica G. Peano, Università di Torino, Italy) |
| Francesca Cioffi (Dipartimento di Matematica e Applicazioni R. Caccioppoli, Università di Napoli Federico II, Italy) |