# Welcome

Welcome to my personal website, which is permanently “under construction”, and where I collect some things that interest me, some things about me, and some completely unrelated things.

## Interests

### Computer Science

I’m broadly interested in building systems for reasoning and inference tasks. Currently, together with the team at Vaticle, we are trying to build a better framework for the representation and synthesis of structured knowledge.

### Mathematics

I have worked on graphical calculi for category theory and type theory (going back to ideas of Penrose), and generalizations thereof called manifold diagrams. My work helped kickstart the theory of geometric higher categories, a young area lying at the intersection of stratified geometry, combinatorial topology and higher algebra. To get a quick overview, check out my nine short stories about geometric higher categories. Many parts of the area remain under active development. My long term ambition for this line of research would be to provide new foundations for Quantum Topology and Mathematical Physics, as well as a basis for higher-categorical reasoning.

## Career highlights

- From 2010 to 2013, I studied Physics at ETH Zurich. I received the Polya Prize for finishing top of my class.
- From 2013 to 2014, I studied Mathematics at Cambridge funded by the German Academic Scholarship Foundation. I focused on Quantum Computation, Information Theory and Category Theory. I received the Parks Prize in Mathematics for finishing top among my college peers.
- In 2014, I started a PhD programme at the Department of Computer Science in Oxford funded by the EPSRC. I submitted my thesis in late 2018, and defended in early 2019. I also spent time in Maths (where my supervisor was).
- In Mar 2019, I started a 4-year Post-Doc at the Mathematical Institute in Oxford funded by the EPSRC.
- In Dec 2021, I co-wrote a book on the of the foundations of combinatorial directed space.
- In Aug 2022, I co-wrote a paper on the local models of geometric higher categories.

## News

### The Past

- 13 May 2023. New draft of expository paper: from zero to manifold diagrammatic-higher categories
- 28 April 2023. Substantial update to post On pattern matching, computation and (geometric) dependent type theory
- 7 April 2023. Added two notes: On Unification in Mathematics and on Turing computation in (Geometric) Type Theory
- 3 April 2023. About to start a new job as ‘Head of Research’ at Vaticle
- 13 March 2023. New article An invitation to geometric higher categories
- 21 February 2023. New note: a Mazur manifold as a tangle.
- 10 February 2023. Drafted expository article: nine short stories about geometric higher categories.
- 10 January 2023. Talk at the QTCat Seminar in Hamburg on “Geometric Higher Categories”. handwritten notes
- 09 Nov 2022. Oxford mathematics research case study and corresponding tweet (with video) about our work
- 04 Nov 2022. Talk at Oxford Maths Fridays@4 on “Illustrating Mathematics”. Follow-along document Example Files
- 25 Oct 2022. Drafted two (fun) new notes: “towards computable manifolds” and “principles of higher-dimensional logic”.
- 13 Sep 2022. New paper draft: “A brief introduction to framed combinatorial topology”.
- 30 Aug 2022. Chris Douglas and I uploaded the “Manifold diagrams and tame tangles” preprint. It is accompanied by a note on the D4 singularity.
- 02 Jun 2022. I gave a talk at the Geometric Structures Lab at the Fields Institute, University of Toronto. Here’s the video
*(password: #d8=Wm40vV where # is the lowest dimension in which exotic smooth spheres have been constructed)*. - 16 Mar 2022. I gave a talk at the TQFT Club at the University of Lisbon. Here’s the video.
- 29 Dec 2021. Chris Douglas and I uploaded the FCT book preprint
- 22 Nov 2021. I gave a talk in the Advanced topology class on “Generalized differential cohomology theories”.

### The future

- Rest of 2023. preparing a preprint with Lukas Heidemann and Christopher Douglas

## Comment policy

Comments are enabled for most online notes (and some other pages on this website). Relevant and respectful comments are most welcome. You can also write mathematics in the comments.