Modular Lattices in Euclidean Spaces

Spatial Analysis in curved spaces with Non-Euclidean Geometry

The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...

Euclidean Lattices: Algorithms and Cryptography

Euclidean lattices are a rich algebraic object that occurs in a wide variety of contextsin mathematics and in computer science. The present thesis considers several algorithmicaspects of lattices. The concept of lattice basis reduction is thoroughly investigated: in par-ticular, we cover the full range of time-quality trade-offs of reduction algorithms. On thefirst hand, we desc...

Berkovich Spaces Embed in Euclidean Spaces

Let K be a eld that is complete with respect to a nonarchimedean absolute value such that K has a countable dense subset. We prove that the Berkovich analyti cation V an of any d-dimensional quasi-projective scheme V over K embeds in R. If, moreover, the value group of K is dense in R>0 and V is a curve, then we describe the homeomorphism type of V an by using the theory of local dendrites.

On quasiplanes in Euclidean spaces

A variational inequality for the images of k-dimensional hyper-planes under quasiconformal maps of the n-dimensional Euclidean space is proved when 1 ≤ k ≤ n − 2 .

Equiangular lines in Euclidean spaces