13 January 2017:
We had a hugely productive meeting on Wednesday and I'm really excited about the new ideas:
* The connection between Brandon Coya's work on bond graphs and Ross Street's work on weak bimonoids, noticed by Brendan, is really fascinating - it implies that there's a "quantum groupoid" associated to electrical circuits, and it implies that our conjectured list of axioms characterizing the category of bond graphs was missing some highly nonobvious relations.
* Daniel Cicala is revisiting Franciscus Rebro's work on the bicategory of cobordisms and will prove it's a symmetric monoidal bicategory.
* Kenny Courser had the smart idea of revisiting Jeffrey Morton and Jamie Vicary's work on Khovanov's categorified Heisenberg algebra and making it rigorous using our new ability to get ahold of symmetric monoidal bicategories, and I realized we can actually do this.
* Adam Yassine seems to have proved that there's a bicategory of symplectic manifolds and cospans whose legs are Poisson fibrations — good for the study of open systems in classical mechanics.
And that's not all! In our Metron project,
* Blake Pollard and John Foley are developing a new framework for search and rescue operations (and many other distributed optimization problems).
* Joseph Moeller created a new algebraic structure generalizing the "operad for communication networks", and I think we can prove this new structure has an elegant category-theoretic description.
It's all great stuff. But these weekly reports are supposed to be about things that have been completed, just to focus your attention on getting things finished. So here are two things like that:
* The math department at U.C. Riverside is hosting the Fall Meeting of the AMS Western Section on Saturday and Sunday, Nov. 4 and 5, 2017. My proposal for a special session on **Applied Category Theory** has been accepted! I hope you submit proposals for talks — if you're able to come despite the fact that, as usual for such meetings, we have no money. I'll say in a while how you can propose a talk: there will be a webpage where you can do this.
* U. C. Riverside has agreed to be a repository of climate data collected by the Azimuth Backup Project. This means we don't have to figure out how to hold this data permanently. We've raised over $10,000 by now, so we're fine in the short term.