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 ...

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 ...

We introduce DWZ (Derksen-Weyman-Zelevinsky) mutation for a special class of SPs (species with potential). Generalizing a construction of Labardini-Fragoso, we associate with each triangulated, constantly weighted orbifold ...

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 ...

Using adiabatic limits of Eta invariants, Rho invariants of the total space of a fiber bundle are investigated. One concern is to formulate the aspects of local index theory for families of Dirac operator in terms of the ...

In dieser Arbeit werden erstmalig über einen zur Nichtstandardform gehörenden Erzeugendensystem-Ansatz robuste Wavelet-basierte Multiskalen-Löser für allgemeine zweidimensionale stationäre Konvektions-Diffusions-Probleme ...

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 ......

Low-rank tensor recovery is an interesting subject from both the theoretical and application point of view. On one side, it is a natural extension of the sparse vector and low-rank matrix recovery problem. On the other ...

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 ......