Reflections on “glue work”| theHigherGeometer
Good news everyone! Even *longer* running halting Turing machines with just six states.| theHigherGeometer
Is this the oldest example of the well-foundedness of the naturals being explicitly mentioned?| theHigherGeometer
Following on from last post I want to talk about the appropriate notion of morphism between the objects I defined. Recall that these are Lie groupoids with a map to the manifold satisfying some properties ( and are surjective submersions), and then equipped with a little bit of extra structure. We will fix a bundle … Continue reading Morphisms between abelian differentiable gerbes| theHigherGeometer
Here’s a fun thing: if you want to generate a random finite space, instead select a random subset from , the -fold power of the Sierpinski space , since every space embeds into some (arbitrary) product of copies of the Sierpinski space. (Recall that has underlying set , and the only open subsets are . … Continue reading Small fun observation about finite topological spaces, and some challenges| theHigherGeometer
Bundle gerbes are a class of objects that are my bread and butter, but there are many different ways of thinking about them. In my paper with Raymond Vozzo we wrote a different take that starts from the point of view of plain Lie groupoids (which we allow to be infinite-dimensional) and slowly builds in … Continue reading Abelian differentiable gerbes – recap| theHigherGeometer
In my current day job, I’m involved in the development of a research-based software tool, where the language being used is Haskell. While I can’t talk about the specifics of either the tool or the mathematics as yet, there was something interesting that we had to go through last month in the development process. As … Continue reading Type-theoretic considerations in functional language software development| theHigherGeometer
I got an email the other day from mathematician Bogdan Grechuk, whose book Polynomial Diophantine Equations: A Systematic Approach ( was recently released. This is to my mind a rather remarkable bo…| theHigherGeometer
This talk, titled Allons-nous continuer la recherche scientifique? [Will we continue scientific research?] is rather different. It’s not a mathematics research talk, but a sociological one, based on Grothendieck’s marked shift in personal motivations. This talk survived as a scratchy audio recording, and I had no idea that it had been transcribed, let alone subsequently … Continue reading Transcription and translation of Grothendieck’s 1972 CERN talk| theHigherGeometer
Nearly 11 years ago I spoke with the then editor-in-chief of the open access journal Theory and Applications of Categories (TAC) about the option of registering Digital Object Identifiers (DOIs) fo…| theHigherGeometer