Merlin's Notebook

During Thanksgiving week I went to Wytham Abbey, a manor house in Oxfordshire where the “Workhop on Non-Compositionality in Complex Systems” was taking place. The workshop (organized by Matteo Cappucci and Jules Hedges) was centered around four papers that covered the theme of compositional patterns and emergence therein. I wrote one of them (the one… Read more

Hi Mike, You asked: “[w]hat is the analog of tree-width for finite permutation groups? This should have an answer. And the answer should be fairly obvious/deducible (Cf Grothendieck) from the right abstract point of view.“ This blog post is part of my correspondence with Mike Fellows. I’m posting it here for three reasons: (1) I… Read more

Sometimes in math things sound obviously true and that’s exactly how it turns out. Other times, you’re less lucky. Today was one of those days. In this post we’ll see that, although \(\mathsf{Grph}\) is adhesive, \(\mathsf{Grph}^{op}\) isn’t. For a while now, Will Turner and I have been working both with adhesive categories and with \(\mathsf{Grph}^{op}\).… Read more

Towards the end of May I visited Johannes Carmesin‘s group at the University of Birmingham. I was there to work with Will Turner on obstructions to compositionality and their categorification. I had an absolute blast. Will and I proved a bunch of new results and this post is about one of them: I’ll tell you… Read more

Last fall I read “A diagrammatic view of differential equations in physics” by Evan Patterson, Andrew Baas, Timothy Hosgood and James Fairbanks. They show that you can use diagrams to write down the sorts of equations on manifolds that physicists care about. In this post I’ll try to convey the main ideas of the paper… Read more

In a previous post, we discussed sieves, the sieve-y definition of Grothendieck topologies and a few exaples thereof. Today we’ll return to sheaves, but this time we do so armed with a better understanding of sites (the “places” in which to define sheaves). This post consists of notes and reflections from reading Daniel Rosiak’s book… Read more