28 July 2017:
This week's progress!
1) First, some good news from Jason Erbele:
> A. Just a quick reminder that I will be attending the [Hopf Algebras etc.](https://www.perimeterinstitute.ca/conferences/hopf-algebras-kitaevs-quantum-double-models-mathematical-connections-gauge-theory) conference at the Perimeter Institute this coming week. Based on the list on the conference website, just under 50 people are participating. The relatively small crowd should make it a bit easier for me to meet people and network, despite not being one of the speakers.
> B. I haven't gotten word one way or the other yet regarding the Air Force Research Laboratory postdoc in Dayton, OH, but I have been invited to spend a couple of days at the beginning of September at U. Penn. to get to know some of the people that I would be working with, assuming I do get the job. It'll be Tuesday and Wednesday, September 5-6. They also want me to give a talk, and Dan Koditschek had this to say about it:
> > "[M]y suggestion would be that you aim for a 45 min. talk with your major effort being to explain the nature and impact (as distinct from the details of the technical accomplishments) of your ideas and results to an audience interested in but very unfamiliar with your area. My group is typically quite active and you will likely be interrupted throughout with questions."
> You will likely recall that Dan Koditschek is the head of the group that Brendan was with before he took David Spivak's offer at MIT.
The second item is especially promising. He's telling you to focus on the big picture and not sink into too many technical details, and he's telling you to discuss the "impact" of your work, which means you have to make it sound like a big deal. I urge you to get some advice from Brendan about how to do this, because he knows Koditschek. He also knows Sobocinski
and company, who seem to be doing a reasonable job of convincing people of the importance of their work.
In trying to sell your ideas and accomplishments, it will help to interpret "your" rather broadly, to include the work of Bonchi, Sobocinski and Zanasi on similar themes. I don't mean to pretend you did their work - you should of course credit them. But you should learn their work, and if they've done interesting things, especially "practical" things, you should feel free to explain those things in your talk.
In short, **think of yourself not as a mere individual, but as a representative of a movement**. If the movement is doing interesting things, and you represent it ably, Koditschek may want to hire you - to have "someone who knows that stuff" around, especially now that Brendan is no longer there.
2) Second, Nina Otter is at a workshop on [Macaulay2](https://sites.google.com/view/macaulay2-gatech-2017/home), which is a software package
for algebraic geometry. I get the feeling that this workshop is focused on using
Macaulay2 in statistics, phylogenetics and other areas - "applied algebraic geometry".
3) Third, Blake and I put our paper on [A compositional framework for Markov processes](https://arxiv.org/abs/1704.02051) into the suitable format for _Reviews in Mathematical Physics_ and gave it to that journal. They should give us the proofs back in a week or two.
4) Fourth, Brandon and Franciscus and I put our paper on [Props in network theory](https://arxiv.org/abs/1707.08321) onto the arXiv. Shortly afterward, I got a comment from the category theorist Thomas Holder. He said:
> Please excuse me for making a couple of comments on your arXiv.1707.08321. For one your first reference in the bibliography is empty.
This proves that the first thing people do is look at your bibliography. I fixed this.
> The other thing is, since you pay considerable attention to the history of the subject, I'd like to point out that the use of monoidal categories in network theory including the use of string diagrams was pioneered by the German computer scientist Günter Hotz in 1965/66 and that by the end of the 1960s there was considerable activity by his group in Saarbrücken with some nice results e.g. Hans Langmaarck discovered the first ordering of the braid group in the process of giving normal forms for the morphisms in 1969. At the same time this was taken up by a research group in East Germany around the algebraicist Lothar Budach, a former student of Krull's, in collaboration with Hans-Joachim Hoehnke leading to a monumental monograph on 'Automaten und Funktoren' in 1975. David Benson at that time also worked in this framework.
> Most of this work is unfortunately in German (e.g. a monograph of Hotz on 'Schaltkreistheorie' or Boolean circuit theory in 1974) - you find some of the relevant references at the nLab entry on Hotz.
> Permit me to unload here an observation which for a lack of proper understanding of QFT I've never known much what to make of: One of the results in the Budach-Hoehnke book is a generalization of the Chomsky normal form for context-free grammars which says that the morphisms (=syntactical derivations) in the monoidal category corresponding to your (not necessarily context-free) grammar have a normal form provided the rewriting rules that generate your category don't include at the same time a (creation) rule that rewrites the empty string to a non empty string e->X1...Xn and the reverse annihilation rule X1...Xn->e. This suggests that (at least to a non cognoscente like me) that renormalization of a QFT is tied to the normalization of the corresponding theory of Feynman diagrams.
> thanks for your patience&best wishes Thomas Holder
Personally I think the relation between "normalization of strings" and "renormalization in QFT" is mainly just a pun, but the remarks on Hotz are interesting and I may decide to add something about his work to our paper.