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

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.