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Curvature bounds and heat kernels: discrete versus continuous spaces
We introduce and study rough (approximate) lower curvature bounds and rough curvature-dimension conditions for discrete spaces and for graphs. These notions extend the ones introduced in \cite{St06a} and \cite{St06b} ...
Type III von Neumann algebras in the Theory of Infinite-dimensional Groups
We study two examples of von Neumann algebras that are generated by the right and left regular representations of two infinite dimensional groups $\BON$ and $\BOZ$. These regular representations were studied by Alexander ...
Numerical Methods for a Reduced Model in Thin-Film Micromagnetics
We address the conformal finite element approximation to a reduced 2-d model arising in thin-film micromagnetics. The model was derived by DeSimone, Kohn, Müller, and Otto for a thin-film ferromagnetic element under an ...
Stability conditions on derived categories
My thesis is divided into two parts. In the first part I consider stability conditions on the derived category of complex manifolds without any nontrivial subvarieties. In particular, I construct and classify stability ...
Anisotrope Verfahren in der Bildverarbeitung: Gradientenflüsse, Level-Sets und Narrow Bands: Gradientenflüsse, Level-Sets und Narrow Bands
Isotrope Glättungs- und Restaurierungsverfahren neigen dazu, Isoflächen abzurunden. Für beispielsweise ecken- oder kantenerhaltendes Glätten oder Restaurieren sind sie nicht geeignet. Stattdessen können anisotrope ...