Convergence in some ringed toposes
We study the spectral convergence of compact Riemannian manifolds in relation with the Gromov-Hausdorff distance and discuss the geodesic distances and the energy forms of the limit spaces.
Iterative approximation algorithms are successfully applied in parametric approximation tasks. In particular, reduced basis methods make use of the so-called Greedy algorithm for approximating solution sets of parametrized partial differential equations. Recently, a priori convergence rate statements for this algorithm have been given (Buffa et al. 2009, Binev et al. 2010). The goal of the current study is the extension to time-dependent problems, which are typically approximated using the POD–Greedy...
These are the lecture notes of a minicourse given at a winter school in Marseille 2011. The aim of the course was to give an introduction to recent work on the geometry of the space of Kähler metrics associated to an ample line bundle. The emphasis of the course was the role of convexity, both as a motivating example and as a tool.
We write a cohomological resolution of the sheaf of solutions of the differential operator on a manifold and study the cohomology groups and .