# 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

I’m a computer scientist and mathematician. I’m (mostly) think about building typeful languages for databases, knowledge representation, and reasoning, and (infrequently) about type-theoretic-geometric languages for mathematical foundations and topology.

### Computer Science

Together with the team at TypeDB, I’m working on building high-level database systems, that can faithfully and intuitively represent the diverse information of real-world application domains. Type theory is a guiding principle in this endeavour, which involves the design of a new query language and the implementation of a modern distributed database. More broadly, I’m interested in building systems for reasoning and inference tasks, and excited about the many possibilities that were enabled by recent progress in neural-network-based artificial intelligence.

### Mathematics

I work on geometric (a.k.a. *diagrammatic*) calculi for category theory and type theory (going back to ideas of Penrose and related, e.g., to Feynman diagrams and topological quantum field theories), and generalizations thereof called manifold diagrams. My work helped kickstart the theory of diagrammatic higher categories, a young area lying at the intersection of stratified geometry, combinatorial topology and higher algebra. Many parts of the area remain under active development—the long term ambition for this line of research would be to provide new mathematical foundations for Mathematical Physics as well as a basis for higher-categorical foundations of mathematics.

## 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 diagrammatic higher categories.
- In Apr 2023, I started a position as Head of Research at TypeDB
- In Mar 2024, I started a Associate Researcher position at the Mathematical Institute, University of Oxford (part-time—I’m still working full-time on TypeDB!)

## News

### The Past

- 04 Mar 2024. Our
`TypeQL`

paper got accepted at ACM SIGMOD/PODS’24! We hope to see you in Santiago de Chile later this year. - 14 Jan 2024. I gave a lengthy ~2h talk on TypeDB’s data model, the last talk in our Fundamentals lecture series.
- 26 Nov 2023. We gave a Tech Talk at the Cambridge Computer Laboratory!
- 16 Nov 2023. I gave the first talk of our TypeDB Fundamental Lecture series.
- 15 Nov 2023. I gave an invited talk on manifold-diagrammatic mathematics (video) at the Center for Quantum and Topological Systems at NYU Abu Dhabi.
- 20 Oct 2023. We presented at ACM CIKM. Thank you to Ingo Frommholz for hosting our session!
- 15 Sep 2023. Our new TypeDB website launched! To also checkout our docs. Any feedback is much appreciated.
- 8 Jun 2023. Christoph Weis and I published a little project on the topic of deep reinforcement learning: HexBot !
- 1 Jun 2023. I gave a talk in the TallCat Seminar of Tallinn University of Technology titled “From zero to manifold diagrams” (video recording)
- 13 May 2023. New draft of expository paper: from zero to manifold diagrammatic-higher categories
- 3 April 2023. About to start a new job as ‘Head of Research’ at TypeDB
- 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 diagrammatic 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

- TBD

## 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.