Christoph Dorn

Building typeful databases at TypeDB.

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Future pathways in diagrammatic mathematics: from Computable Manifolds to Quantum Gravity

Comments first published

This short note takes a birds-eye perspective on motivations for working as a researcher in mathematics and physics (which are first and foremost motivations personal to me, but I think they may be shared with many others). I briefly round up some (glimmers of) potentially interesting projects that I find fascinating. The note is written on the occasion on moving on to other endeavors. → read note

Mazur manifold as tangle diagram

Comments first published

Mazur manifolds are intimately related to homology spheres, and are part of the puzzling world of 4-manifolds. Here we construct the simplest example of a Mazur manifold as a tangle diagram. → read note

Principles of higher-dimensional logic

Comments first published

We allow ourselves to speculate a bit about how the 1-dimensional logical constructs that one frequently encounters in practical approaches to mathematical foundations may in fact emerge from a set of “more fundamental” principles of compositionality in higher-dimensional logic. → read note

Towards computable manifolds

Comments first published

In this (exceedingly brief) note, we discuss computability questions in the context of manifold theory. The main observation is that several computabilty issues in classical “set-point (differential) topological” foundations may potentially be overcome when working with manifolds from the higher-categorical perspective of manifold diagrams and tangles. → read note