Dr Christoph Dorn
I'm a part-time post-doc working on diagrammatic algebra, my "main time" is spent in software and AI.
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
- Conference paper : TypeQL: A Type-Theoretic & Polymorphic Query Language, 2024, 27 pages
- Survey paper : Nine short lectures on geometric higher categories, 2023, 33 pages
- Expository paper : Introduction to framed combinatorial topology, 2022, 25 pages, joint w/ Christopher Douglas
- Paper : Manifold diagrams and tame tangles, 2022, ~110 pages, joint w/ Christopher Douglas
- Book : Framed combinatorial topology, 2021, ~460 pages, joint w/ Christopher Douglas (to be published by the AMS, 2026)
- Thesis : Associative n-categories, 2019
- "Diagrammatic Mathematics Club" (MT25-HT26, Organizer .. email me or C. Douglas for more info!)
- Mini-course on Framed Combinatorial Topology (TT21, Lecturer)
- Category Theory (MT20, Teacher)
- Algebraic Topology (MT19, Teacher)
- Categories, Proofs and Processes (MT16, Teacher)
- Topology (HT16, Tutor)
- Complexity Theory (HT16, Teacher + TA)
- Automata, Logic and Games (MT15, Teacher + TA)
- College Scholarship for Sciences, St Catherine's College, Oxford University
- 3 Year EPSRC Scholarship by Oxford Department of Computer Science, Oxford University
- Bateman Scholar, Trinity Hall, Cambridge University
- Parks Prize for Mathematics by Trinity Hall, Cambridge University
- 4 Year Scholarship by German National Academic Foundation
My research develops computable foundations for geometry and higher algebra. This line of research studies purely combinatorial, diagrammatic calculi of stratified manifolds, their singularities and higher Morse structures. The research establishes a fundamental bridge between combinatorics and conceptions of manifold theory and higher algebra. Yet more broadly, it provides a unified approach to computational representation and processes (via diagrams and diagrammatic rewriting).
More recently, I have been working in database theory, query languages and optimization. And yet more recently, I have been working on connections to meta-training and architecture of neural networks, to enable the step from "evolution to know" to "evolution to learn to know".