6 January 2018:

Here is this week's progress, as far as I know:

1) Brandon will be doing a job interview for a visiting position at Colorado College! The interview will be at the Joint Mathematics Meetings in San Diego next week.

2) John Foley is giving at talk on Thursday at the Joint Mathematics Meetings!

* John Foley, Modeling the composition of networks with operads

> **Abstract.** Networks can be combined in many ways including by overlaying one on top of another or sitting one next to another. We encode these two ways of combining networks as a specific kind of functor and prove that the application of a novel general construction to these functors results in typed operads. The class of operads we construct - which we call network operads - contains a wealth of examples whose many to one operations serve as a syntax for designing complex networks by composing simpler networks. We give examples of concrete ways to compose networks with our setup by matching specific kinds of networks to actions of network operads. Remarkably network operads can provide a unified treatment of the structural design and behavioral tasking of dynamic networks.

I guess some of you may miss our Wednesday meeting due to that conference. The rest of us should still have tons to talk about.

3) Daniel and Kenny's paper has appeared on TAC! As the saying goes, "the operad isn't over until the fat lady sings"... but now she has sung! View it in its full published beauty:

* Daniel Cicala and Kenny Courser, [Spans of cospans in a topos](http://www.tac.mta.ca/tac/volumes/33/1/33-01.pdf).

> **Abstract.** For a topos T, there is a bicategory MonicSp(Csp(T)) whose objects are those of T, morphisms are cospans in T, and 2-morphisms are isomorphism classes of monic spans of cospans in T. Using a result of Shulman, we prove that MonicSp(Csp(T)) is symmetric monoidal, and moreover, that it is compact closed in the sense of Stay. We provide an application which illustrates how to encode double pushout rewrite rules as 2-morphisms inside a compact closed sub-bicategory of MonicSp(Csp(Graph)).

4) I invited Kathryn Hess and Steve Lack to join the advisory board of a new journal on applied category theory called Compositionality, and they accepted. Bob Coecke, Valeria de Paiva and I are also on the advisory board. It seems like the people actually doing the work to set up this journal are Brendan Fong, Nina Otter and Joshua Tan. A guy named [Ilyas Khan](http://cambridgequantum.com/team-ilyas-khan/) of Cambridge Quantum Computing Inc. is providing the financial support - apparently he likes category theory!

This journal should start publishing around June, and this could be a good place to submit papers.

5) I got invited to speak at a conference called [Symmetries, Observables, and the Noether's Theorems: A 100th Anniversary Conference for the Work of Emmy Noether](https://philosophy.nd.edu/news/events/noether/) at Fischer Hall in London Oct 5-6 2018. They asked me to speak about category-theoretic aspects of Noether's theorem on symmetries and conserved quantities. I may go, because I love Noether's theorem and this would give me an excuse to think about it harder. Plus, a bunch of cool people will be there. The ones I know are Yvette Kosmann-Schwarzbach, Harvey Brown, Jeremy Butterfield, Rob Spekkens, and Frank Wilczek (who won the Nobel prize for his work on confinement in quantum chromodynamics).

6) I got invited to speak at a workshop called [Open Research: Rethinking Scientific Collaboration](https://www.perimeterinstitute.ca/conferences/open-research-rethinking-scientific-collaboration), which will be held at Perimeter Institute in Waterloo, Ontario on March 26-28, 2018. It sounds great; unfortunately I'll be busy.

7) I got invited to speak at a workshop with a very long title: [Workshop on Higher Gauge Theory: Where should we look for higher gauge matter? (From emerging physics and topological quantum computing to string and M-theory)](http://www1.maths.leeds.ac.uk/%7Eppmartin/SEMINARS/HGT_WS/index.html), which is being held in Leeds, England on Feb. 28 - March 2. I'm not doing this stuff anymore so I won't go. Luckily my student John Huerta is going, and so is Urs Schreiber.

Christian Saemann will be there too: he recently used a categorified Lie algebra from my student Alissa Crans' thesis to make a concrete proposal for a mysterious 6-dimensional field theory that seems crucial for unifying M-theory, Khovanov homology and the geometric Langlands correspondence! I blogged about this here:

* [An M5-brane model](https://golem.ph.utexas.edu/category/2017/12/an_m5brane_model.html).

His proposal may not be right, but this is way-cool stuff.

8) I edited my paper [Struggles with the continuum](http://math.ucr.edu/home/baez/continuum.pdf) in accord with the referee's suggestions, and sent it back. I hope it's done, but I'm not sure.

Here is this week's progress, as far as I know:

1) Brandon will be doing a job interview for a visiting position at Colorado College! The interview will be at the Joint Mathematics Meetings in San Diego next week.

2) John Foley is giving at talk on Thursday at the Joint Mathematics Meetings!

* John Foley, Modeling the composition of networks with operads

> **Abstract.** Networks can be combined in many ways including by overlaying one on top of another or sitting one next to another. We encode these two ways of combining networks as a specific kind of functor and prove that the application of a novel general construction to these functors results in typed operads. The class of operads we construct - which we call network operads - contains a wealth of examples whose many to one operations serve as a syntax for designing complex networks by composing simpler networks. We give examples of concrete ways to compose networks with our setup by matching specific kinds of networks to actions of network operads. Remarkably network operads can provide a unified treatment of the structural design and behavioral tasking of dynamic networks.

I guess some of you may miss our Wednesday meeting due to that conference. The rest of us should still have tons to talk about.

3) Daniel and Kenny's paper has appeared on TAC! As the saying goes, "the operad isn't over until the fat lady sings"... but now she has sung! View it in its full published beauty:

* Daniel Cicala and Kenny Courser, [Spans of cospans in a topos](http://www.tac.mta.ca/tac/volumes/33/1/33-01.pdf).

> **Abstract.** For a topos T, there is a bicategory MonicSp(Csp(T)) whose objects are those of T, morphisms are cospans in T, and 2-morphisms are isomorphism classes of monic spans of cospans in T. Using a result of Shulman, we prove that MonicSp(Csp(T)) is symmetric monoidal, and moreover, that it is compact closed in the sense of Stay. We provide an application which illustrates how to encode double pushout rewrite rules as 2-morphisms inside a compact closed sub-bicategory of MonicSp(Csp(Graph)).

4) I invited Kathryn Hess and Steve Lack to join the advisory board of a new journal on applied category theory called Compositionality, and they accepted. Bob Coecke, Valeria de Paiva and I are also on the advisory board. It seems like the people actually doing the work to set up this journal are Brendan Fong, Nina Otter and Joshua Tan. A guy named [Ilyas Khan](http://cambridgequantum.com/team-ilyas-khan/) of Cambridge Quantum Computing Inc. is providing the financial support - apparently he likes category theory!

This journal should start publishing around June, and this could be a good place to submit papers.

5) I got invited to speak at a conference called [Symmetries, Observables, and the Noether's Theorems: A 100th Anniversary Conference for the Work of Emmy Noether](https://philosophy.nd.edu/news/events/noether/) at Fischer Hall in London Oct 5-6 2018. They asked me to speak about category-theoretic aspects of Noether's theorem on symmetries and conserved quantities. I may go, because I love Noether's theorem and this would give me an excuse to think about it harder. Plus, a bunch of cool people will be there. The ones I know are Yvette Kosmann-Schwarzbach, Harvey Brown, Jeremy Butterfield, Rob Spekkens, and Frank Wilczek (who won the Nobel prize for his work on confinement in quantum chromodynamics).

6) I got invited to speak at a workshop called [Open Research: Rethinking Scientific Collaboration](https://www.perimeterinstitute.ca/conferences/open-research-rethinking-scientific-collaboration), which will be held at Perimeter Institute in Waterloo, Ontario on March 26-28, 2018. It sounds great; unfortunately I'll be busy.

7) I got invited to speak at a workshop with a very long title: [Workshop on Higher Gauge Theory: Where should we look for higher gauge matter? (From emerging physics and topological quantum computing to string and M-theory)](http://www1.maths.leeds.ac.uk/%7Eppmartin/SEMINARS/HGT_WS/index.html), which is being held in Leeds, England on Feb. 28 - March 2. I'm not doing this stuff anymore so I won't go. Luckily my student John Huerta is going, and so is Urs Schreiber.

Christian Saemann will be there too: he recently used a categorified Lie algebra from my student Alissa Crans' thesis to make a concrete proposal for a mysterious 6-dimensional field theory that seems crucial for unifying M-theory, Khovanov homology and the geometric Langlands correspondence! I blogged about this here:

* [An M5-brane model](https://golem.ph.utexas.edu/category/2017/12/an_m5brane_model.html).

His proposal may not be right, but this is way-cool stuff.

8) I edited my paper [Struggles with the continuum](http://math.ucr.edu/home/baez/continuum.pdf) in accord with the referee's suggestions, and sent it back. I hope it's done, but I'm not sure.