Syzygies, from Theory to Applications

The classical results and open problems that lie at the interface between commutative algebra and algebraic geometry, have undergone a striking evolution over the last quarter of a century, aided in large part by computer algebra calculations. At the heart of all these developments is the concept of syzygies: the analysis of the algebraic relations (syzygies) between the equations defining a geometric object leads to deep insights of its geometric properties. The aim of this CIMPA research school is precisely to introduce graduate students and young researchers to some fundamental techniques and recent developments on syzygy-based methods, including their application to combinatorial and toric geometry, module of differentials, the Minimal Resolution Conjecture, regularity of powers of ideals, geometric properties of rational maps and geometric modeling. Besides the six courses, computational and problem solving sessions are planned in order to train the students to the use of free computer algebra systems.