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.
Administrative and scientific coordinators
Course 1: "The ubiquity of Syzygies", Aron SIMIS (Universidade Federal de Pernambuco, Brazil)
Course 2: "Computational Algebraic Geometry", Hal SCHENCK (Iowa State University, USA)
Course 3: "Module of Differentials, Jacobian Criterion, Evolutions, Reductions, Briançon-Skoda Theorem, and Vector Fields", Claudia POLINI (University of Notre Dame, USA)
Course 4: "Geometry of syzygies", Marc CHARDIN (CNRS and University Pierre et Marie Curie at Paris, France)
Course 5: "Syzygies of rational maps with applications to geometric modeling", Laurent BUSÉ (Inria, France)
Course 6: "The minimal resolution conjecture for points on projective varieties. Applications.", Rosa Maria MIRÓ-ROIG (Universidad de Barcelona, Spain)
Website of the school
How to participate
For registration and application to a CIMPA financial support, follow the instructions given here.
Deadline for registration and application: May 31, 2019.