# Framed Combinatorial Topology

`Framed combinatorial topology’ is the title of a book we just uploaded to the arXiv. On the linked page you’ll find more information!

The project is part of the larger endeavor of geometric higher category theory.

Researcher at Vaticle.

- United Kingdom
- Vaticle
- Oxford Math
- Oxford CS
- Cambridge Math
- ETH Physics
- GitHub

`Framed combinatorial topology’ is the title of a book we just uploaded to the arXiv. On the linked page you’ll find more information!

The project is part of the larger endeavor of geometric higher category theory.

Comments first published

Pattern matching is an ubiquitous tool in theoretical computer science and type-theoretical mathematics, as well as the formalization of formal languages themselves. We briefly review its role in these subjects, giving examples along the way. We then motivate a deeper connection between pattern matching and higher-dimensional geometry, and suggest how geometric type theory, while not a real type theory yet, tries to provide a general formal framework in which mathematics can be built from higher-dimensional patterns. → read note

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

first published

Fast and mathematically self-contained introduction to basic ideas in geometric higher category theory, written up as an article for the n-Category Café. → go to link

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