Title: Recent progress on the computation of Riemann-Roch spaces.
Abstract: Riemann-Roch spaces are vector spaces of rational functions
whose poles and zeros are constrained by points lying on a curve. They are
important objects in algebraic geometry and have found many applications
in diophantine equations, symbolic integration and algebraic geometry
codes. In the first part of this talk, I will present the Brill-Noether
framework to compute Riemann-Roch spaces and explain how to design an
efficient subquadratic algorithm using adequate tools from computer
algebra. In a second part, we will discuss another approach used in Hess’
algorithm and provide new complexity bounds for precomputations required
by this method. The first part is joint work with Alain Couvreur and
Grégoire Lecerf.
