1 Definitions Definition 1. A graded ring is a ring S together with a set of subgroups Sd, d ≥ 0 such that S = ⊕ d≥0 Sd as an abelian group, and st ∈ Sd+e for all s ∈ Sd, t ∈ Se. One can prove that 1 ∈ S0 and if S is a domain then any unit of S also belongs to S0. A homogenous ideal of S is an ideal a with the property that for any f ∈ a we also have fd ∈ a for all d ≥ 0. A morphism of graded r...

We study “forms of the Fermat equation” over an arbitrary field k, i.e. homogenous equations of degree m in n unknowns that can be transformed into the Fermat equation Xm 1 +. . .+Xm n by a suitable linear change of variables over an algebraic closure of k. Using the method of Galois descent, we classify all such forms. In the case that k is a finite field of characteristic greater than m that ...

We present a deformable model to reconstruct a surface from a point cloud. The model is based on an explicit mesh representation composed of multiple competing evolving fronts. These fronts adapt to the local feature size of the target shape in a coarse–to–fine manner. Hence, they approach towards the finer (local) features of the target shape only after the reconstruction of the coarse (global...

We develop further the topological theory of regular variation of [BOst13]. There we established the uniform convergence theorem (UCT) in the setting of topological dynamics (i.e. with a group T acting on a homogenous space X), thereby unifying and extending the multivariate regular variation literature. Here, working with realtime topological ‡ows on homogeneous spaces, we identify an index of...