The simulation and analysis of particle systems dynamics is an important subfield of computational materials science. It allows the investigation of many properties of interest, such as reaction mechanisms, diffusion rates, ...

In this dissertation, we study multiplications in globally equivariant stable homotopy theory. Concretely, this means studying ultra-commutative ring spectra, which encode a rich multiplicative structure on a family of ...

In this thesis we study various aspects of hyper-Kähler manifolds and abelian varieties such as their derived categories, sheaves, cycles, and topology. The thesis consists of six parts.
The first part is mostly ...

The Merriman, Bence, and Osher (MBO) scheme -- also known as thresholding scheme -- is a numerical method originally introduced to approximate the evolution by mean curvature flow (MCF). The algorithm produces a time ...

This thesis makes contributions to shape spaces and shape optimization of discrete surfaces. Discrete surfaces are triangle meshes with certain regularity and are ubiquitous in many applications in computer graphics, ...

The infinitesimal counterpart of a Lie group is its Lie algebra: the space of right-invariant vector fields with their Lie bracket. As a vector space, it is isomorphic to the tangent space to the Lie group at the unit. A ......

We consider the problem of constructing fast circuits both for binary addition and And-Or paths. And-Or paths are Boolean functions of the form t₀ ∧ ( t₁ ∨ ( t₂ ∧ ( t₃ ......

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 ...