MACIS 2009: rational solutions of polynomial systems

Organizer

• Éric Schost (The University of Western Ontario, Canada)

Overview

• Problem

  This session addresses computational problems related to rational solutions of systems of polynomial equations, in a very broad sense. Topics include (but are not limited to)

  • decision algorithms for the existence of rational points on algebraic curves or surfaces over Q,
  • point-counting problems over finite fields and their applications to cryptology,
  • effective Galois theory,
  • symmetries of polynomial systems,
  • etc

• Motivation and Importance

  Questions on the effective aspects of rational solutions of polynomials systems are difficult: for instance, over Q, it is still unknown whether the existence of rational solutions can be decided. However, algorithms for special cases (rational solutions on curves), related problems (Galois theory over Q or over functions fields), are constantly being developed. The purpose of this session is to bring together researchers on various aspects of this question.