The Complexity of de Rham Cohomology and Linear Differential Systems

par M. Peter Scheiblechner (Lucerne University)

jeudi 6 févr. 2014, 10:30 → 11:30 Europe/Paris

XR.203 (Bâtiment XLIM)

One approach to the computation of the topological Betti numbers of an algebraic variety is to compute its algebraic de Rham cohomology. Monsky gave a purely algebraic proof of the finite-dimensionality of this cohomology, which relates it with certain systems of ordinary linear differential equations with Laurent polynomial coefficients. His arguments can be turned into an algorithm, whose complexity we want to analyze. For this purpose, we have to understand the bit-complexity of these differential systems. In this talk, we explain the definition of de Rham cohomology and its relation to ordinary differential systems.