In this thesis, we consider a novel unbalanced optimal transport model incorporating singular sources, we develop a numerical computation scheme for an optimal transport distance on graphs, we propose a simultaneous elastic ...

This thesis consists of two parts.
In the first part we are focusing on stratified pseudomanifolds equipped with an iterated edge metric. More specifically, in Chapter 1 we give the basic definitions and review some ...

This thesis deals with the statistical mechanics of lattice models. It has two main contributions. On the one hand we implement a general framework for a rigorous renormalisation group approach to gradient models. This ...

In this thesis, we provide new characterizations for several well-studied large cardinal notions. These characterizations will be of two types. Motivated by seminal work of Magidor, the first type characterizes large ...

In this thesis, we consider gradient models on the d-dimensional discrete lattice. These models serve as effective models for interfaces and are also known as continuous Ising models . The height of the interface is modelled ......

This thesis is concerned with the Hodge-theoretic relation between polarized K3 surfaces of degree d and special cubic fourfolds of discriminant d, as introduced by Hassett.
For half of the d, K3 surfaces associated ......

The main objects under consideration in this thesis are called maps, a certain class of graphs embedded on surfaces. We approach our study of these objects from different perspectives, namely bijective combinatorics, matrix ...

In this thesis we develop highly accurate simulation tools for variably saturated flow through porous media able to take advantage of the latest supercomputing resources. Hence, we aim for parallel scalability to very large ...

In this thesis we show the existence of a stable, smooth pseudoisotopyfunctor and construct in the topological, piecewise linear, and smooth category a zig-zag of natural weak equivalences between the stable pseudoisotopyfunctor ...

This thesis is concerned with two special cases of the singular Brascamp-Lieb inequality, namely, the trilinear forms corresponding to the one- and two-dimensional bilinear Hilbert transform. In this work we study the ...