In this thesis we compute the homology of mapping class groups of orientable and non-orientable surfaces. The surfaces we consider are of genus g, have one boundary curve and m permutable punctures. The ...

Most integers are composite and most univariate polynomials over a finite field are reducible. The Prime Number Theorem and a classical result of Gauß count the remaining ones, approximately and exactly.
In two or ...

This thesis focuses on developing mathematical models utilizing complex biomedical datasets to understand epidemiological and cell-biological processes. The thesis is divided into three primary research articles and addresses ...

In this thesis two models are studied: the Boltzmann equation and the incompressible Euler-Poisson equation. Concerning the Boltzmann equation we analyze the longtime behavior of so-called homoenergetic solutions in specific ......

The surfaces of 3D shapes are discretized by surface meshes that represent them in a processable way. This enables simulations of deforming components in CAE, animations for movies, or representations of human organs to ...

This thesis concerns problems arising in the study of flows of viscous fluids. In the first part, we discuss the interaction of the flow of a viscous fluid with a random array of moving particles in the limit of many ...

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 ......

Placement is a crucial step in the design process of VLSI chips as it has a strong influence on the most important optimization goals, e.g., die size, routability, and cycle time. State-of-the-art logic chips consist of ...

In this thesis, we analyse two different settings in the micromagnetic model, which is a mesoscopic variational model for the description of ferromagnets, more precisely the magnetisation m, which is a local average of ...

This thesis is about the relationship between vertex algebras and Costello-Gwilliam factorization algebras, two mathematical approaches to chiral conformal field theory. Many vertex algebras have already been constructed. ......