27 November 2017:

This week's progress:

1) A total of 77 students applied for the "adjoint school" of Applied Category Theory 2017. 16 were chosen, and I believe they include these lucky folks:

  • Daniel Cicala (part of the group working with Pawel Sobocinski on "Modelling of open and interconnected systems")

  • Jade Master (part of the group working with Martha Lewis on "Compositional approaches to linguistics and cognition")

  • Joseph Moeller (part of the group working with Aleks Kissinger on "Unification of the logic of causality")

2) After 841 days, the referee finally coughed up a report on a paper that Brendan Fong and I had submitted to TAC, A compositional framework for passive linear networks. The report is very detailed, about 8 pages long, and says our paper should be published "in some form" but demands major revisions, mainly shortening the paper. While this is tiresome, I think we can do it, since the referee explains exactly how - and I think our paper will be improved.

This quote says it all:

This paper has a wonderfully interesting subject matter, and with
well-chosen notations and terminology, and a better-structured, more
concise presentation, it could be a "gem". But in its current state, I
found that even though I was motivated to read the paper, and even
though I think I am a pretty close approximation of the intended
audience, it took me many months and lots of stamina to fight my way
through it.

It's worth a bit of extra work to create a "gem".

3) Last Monday I attended Paul-André Melliès' habilitation defense, along with

  • the category theorist / computer scientist Gordon Plotkin

  • the co-inventor of braided monoidal categories and the inventor of combinatorial species, André Joyal,

  • the inventor of linear logic, Jean-Yves Girard,

  • the computer scientist Thierry Coquand who gave his name to the programming language Coq,

  • the mathematician Pierre-Louis Curien, an expert on rewriting theory

  • the mathematician George Gonthier who came up with a fully formalized proof of the 4-color theorem using Coq, and

  • Karine Chemla, an expert on the history of Chinese mathematics who is a friend of Lisa's - I was surprised to see her there!

Paul-André passed his defense, and I spent the rest of the week talking to him about the connection between star-autonomous categories, compact closed categories, Frobenius monoids, topological quantum field theory and logic.

There's a big mystery here: there seems to be some primitive form of logic which has topological quantum field theory and propositional logic as special cases, and we'd like to know why. He wants to invite me to Paris for 3 months sometime to work on this. That would be great.

On Tuesday I gave a talk on "our stuff"

  • Compositionality in network theory

Abstract. To describe systems composed of interacting parts, scientists and engineers draw diagrams of networks: flow charts, Petri nets, electrical circuit diagrams, signal-flow graphs, chemical reaction networks, Feynman diagrams and the like. In principle all these different diagrams fit into a common framework: the mathematics of symmetric monoidal categories. This has been known for some time. However, the details are more challenging, and ultimately more rewarding, than this basic insight. Two complementary approaches are presentations of symmetric monoidal categories using generators and relations (which are more algebraic in flavor) and decorated cospan categories (which are more geometrical). In this talk we focus on the latter.

André Joyal liked it a lot and said he wanted to read some of our papers. Nicholas Behr had some very interesting ideas on chemistry as a stochastic process of graph rewriting (since molecules are like graphs), and pointed me to these papers he helped write:

I think we should work on this stuff, since we've got all the techniques!
I also had a great conversation with Mathieu Anel on how symplectic geometry shows up in both classical mechanics and thermodynamics, which revived my dream of somehow unifying quantum mechanics and statistical mechanics. He gave me some clues that might overcome the obstacles I'd been stuck on.

So, a great visit!