I’m excited! In early December I’m going to a workshop on ‘compositionality’, meaning how big complex things can be built by sticking together smaller, simpler parts:
• Compositionality, 5-9 December 2016, workshop at the Simons Institute for the Theory of Computing, Berkeley. Organized by Samson Abramsky, Lucien Hardy and Michael Mislove.
In 2007 Jim Simons, the guy who helped invent Chern–Simons theory and then went on to make billions using math to run a hedge fund, founded a research center for geometry and physics on Long Island. More recently he’s also set up this institute for theoretical computer science, in Berkeley. I’ve never been there before.
‘Compositionality’ sounds like an incredibly broad topic, but since it’s part of a semester-long program on Logical structures in computation, this workshop will be aimed at theoretical computer scientists, who have specific ideas about compositionality. And these theoretical computer scientists tend to like category theory. After all, category theory is about morphisms, which you can compose.
Here’s the idea:
The compositional description of complex objects is a fundamental feature of the logical structure of computation. The use of logical languages in database theory and in algorithmic and finite model theory provides a basic level of compositionality, but establishing systematic relationships between compositional descriptions and complexity remains elusive. Compositional models of probabilistic systems and languages have been developed, but inferring probabilistic properties of systems in a compositional fashion is an important challenge. In quantum computation, the phenomenon of entanglement poses a challenge at a fundamental level to the scope of compositional descriptions. At the same time, compositionally has been proposed as a fundamental principle for the development of physical theories. This workshop will focus on the common structures and methods centered on compositionality that run through all these areas.
So, some physics and quantum computation will get into the mix!
A lot of people working on categories and computation will be at this workshop. Here’s what I know about the talks so far. If you click on the talk titles you’ll get abstracts, at least for most of them.
The program
| 9 – 9:30 am |
Coffee and Check-In
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| 9:30 – 10:30 am | ||
| 10:30 – 11 am |
Break
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| 11 – 11:20 am | ||
| 11:25 – 11:45 am | ||
| 11:50 am – 12:25 pm | ||
| 12:30 – 2 pm |
Lunch
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| 9:30 – 10:05 am | ||
| 10 am – 10:45 am | ||
| 10:50 – 11:20 am |
Break
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| 11:20 – 11:55 am | ||
| 12 – 12:35 pm | ||
| 12:40 – 2 pm |
Lunch
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| 2 – 3 pm |
Discussion
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| 3 – 3:40 pm |
Azimuth 
This looks incredibly exciting! I am a novice and so much new material leaves me wondering as to how or even if I might ever be able contribute something useful. Nonetheless I see how my computational and topological interests lay in compositionality, and I am very excited by what I’m learning here. Perhaps coincidentally and unrelated, yesterday, random abstract work arrived at the unsolved Non-Existent Complex Six Sphere in a paper dedicated to S.S.Chern, Jim Simons and Nigel Hitchin written by Micheal Atiyah. The connections are fuzzy, I lack some language though I appreciate an ability to array small pieces into complex structures as a logical structure of computation and it appears to me to add high dimensional modularities to “establishing systematic relationships between compositional descriptions complexity.” https://arxiv.org/abs/1610.09366
Doesn’t happen often that I’m sad about dropping out of academia and thus missing a conference or workshop. But this time I am sad. It’s totally aligned with my interests. And many acquaintances attend. David Pym was my boss and collaborator. And Gordon Plotkin once helped me with a decisive grant. Peter Selinger semi-scooped me on “continuations”. Ah well.
With luck some of the lectures will be recorded, or at least slides will be available. I’m sorry you’re not active in this scene, as I’m trying to get up to speed on a lot of the computer science aspects. But you can at least listen in and say something now and then.
I gave a talk at the workshop on compositionality at the Simons Institute for the Theory of Computing next week. I spoke about some new work with Blake Pollard. You can see the slides here:
• John Baez, Compositionality in network theory, 6 December 2016.
and a video here:
This talk assumes considerable familiarity with category theory. For a much gentler talk on the same theme, see:
• Monoidal categories of networks.
Live streaming video of the whole workshop is here:
https://www.youtube.com/channel/UCW1C2xOfXsIzPgjXyuhkw9g
and you can also see recorded talks.
The conference schedule has changed a bit from that shown on my blog article; the revised version is here.
Bill Lawvere figured out a way to talk about syntax versus semantics that even mathematicians—well, even category theorists—could understand. It’s called ‘functorial semantics’. But physicists may not enjoy this idea unless they see it at work in physics. In physics, too, the distinction is important. But it takes a while to understand. I hope Prakash Panangaden’s talk at the start of the Simons Institute workshop on compositionality is helpful:
Here at the Simons Institute workshop on compositionality, my talk on network theory introduced ‘decorated cospans’ as a general model of open systems. These were invented by Brendan Fong, and are nicely explained in his thesis:
• Brendan Fong, The Algebra of Open and Interconnected Systems. (Blog article here.)
But he went further: to understand the externally observable behavior of an open system we often want to simplify a decorated cospan and get another sort of structure, which he calls a ‘decorated corelation’. His talk here explains decorated corelations and what they’re good for:
One of my goals is to turn category theory, and even higher category theory, into a practical tool for science. For this we need good scientific ideas—but we also need good software.
My friend Jamie Vicary has been developing some of this software, and he demonstrated it at the Simons Institute workshop on compositionality. You can watch his demonstration here:
But since Globular runs on a web browser, you can also try it out yourself here:
• Globular.
You can see his talk slides:
• Jamie Vicary, Data structures for quasistrict higher categories. (Talk slides here.)