Paul Großkopf

• Doctor of Philosophy
• PostDoc Position at University of Oxford

Homotopy Quantum Field Theories as variants of Topological Quantum Field Theories are described by functors from some cobordism category, enriched with homotopical data, to a symmetric monoidal category $\mathcal{V}$. A new notion of HQFTs is introduced using target pairs of spaces $(X,Y)$ acounting for basepoints being sent to points in $Y$. Such...

The Knuth Twin Dragon is a compact subset of the plane with fractal boundary of Hausdorff dimension s = (\log \lambda)/(\log \sqrt{2}) , \lambda^{3} = \lambda^{2} + 2 . Although the intersection with a generic line has Hausdorff dimension s-1 , we prove that this does not occur for lines with rational parameters. We further describe the intersectio...

We show that the universal measuring coalgebras between Frobenius algebras turn the category of Frobenius algebras into a Hopf category (in the sense of \cite{BCV}), and the universal comeasuring algebras between Frobenius algebras turn the category Frobenius algebras into a Hopf opcategory. We also discuss duality and compatibility results between...

We show that under mild conditions on the monoidal base category $\mathcal V$, the category ${\sf VHopf}$ of Hopf $\mathcal V$-categories is locally presentable and deduce the existence of free and cofree Hopf categories. We also provide an explicit description of the free and cofree Hopf categories over a semi-Hopf category. One of the conditions...