7 July 2017:

Three pieces of news. The third one is a big deal for me.

1) Brandon has submitted an abstract for our [AMS special session](http://math.ucr.edu/home/baez/ACT2017) on the weekend of November 4-5.

)

* Frobenius monoids, weak bimonoids, and corelations

> **Abstract.** In this talk we consider object 2 in the category FinCorel, whose objects are finite sets and whose morphisms are “corelations.” The object 2 can be equipped with two different Frobenius monoid structures. We show that the two Frobenius monoids interact to form a “weak bimonoid” as defined by Pastro and Street. Baez and Fong have shown that FinCorel is useful for modeling circuits made of wire as morphisms in a category. In this analogy the object 1 is viewed as a single wire. We show how the two Frobenius monoids associated to the object 2 relate to placing pairs of wires into series and parallel connections. (Received July 06, 2017)

2) Kenny and Daniel have finished writing a paper and put it on the arXiv.

* [Bicategories of spans and cospans](https://arxiv.org/abs/1707.02098v1)

> **Abstract.** If C is a category with chosen pullbacks and a terminal object then, using a result of Shulman, we obtain a fully dualizable and symmetric monoidal bicategory Sp(Sp(C))} whose objects are those of C whose morphisms are spans in C, and whose 2-morphisms

are isomorphism classes of spans of spans in C. If C is a topos, the first author has previously constructed a bicategory MonicSp(Csp(C)) whose objects are those of C, whose morphisms are cospans in C, and whose 2-morphisms are isomorphism classes of spans of cospans in C with monic legs. We prove this bicategory is also symmetric monoidal and even compact closed. We discuss applications of such bicategories to graph rewriting as well as to Morton and Vicary's combinatorial approach to Khovanov's categorified Heisenberg algebra.

3) At the end of my trip to Europe I spent a week in Turin at the Institute for Scientific Interchange. This is a research institute with about 56 scientists run by Mario Rasetti, a physicist who used to do statistical mechanics at the Institute for Advanced Studies. 30 years ago he went back to Italy to set up a roughly similar institute in his home town. They study complex networks and data science.

He's been reading our work and liking it. He asked me to set up a mathematics group there!

If I do this, I'll be hiring a number of postdocs to work on networks, applied category theory and the like. That could be some of you - though of course I don't want to hire just my own students; I want to hire the best people I can find. There should also be opportunities for shorter visits, like conferences and workshops, which some of you might attend.

If I do this I won't be giving up my position at UCR, at least not soon. Instead, I'll visit the place repeatedly, for example during summers. Turin is a wonderful city, so I like this idea. But mainly I'm excited at the idea of being able to put together a team of people working on the kinds of math I like.

It's not 100% certain this will happen: I need to decide I really want to do it, and write a proposal, which the board of the ISI will then read, etc.

Three pieces of news. The third one is a big deal for me.

1) Brandon has submitted an abstract for our [AMS special session](http://math.ucr.edu/home/baez/ACT2017) on the weekend of November 4-5.

)

* Frobenius monoids, weak bimonoids, and corelations

> **Abstract.** In this talk we consider object 2 in the category FinCorel, whose objects are finite sets and whose morphisms are “corelations.” The object 2 can be equipped with two different Frobenius monoid structures. We show that the two Frobenius monoids interact to form a “weak bimonoid” as defined by Pastro and Street. Baez and Fong have shown that FinCorel is useful for modeling circuits made of wire as morphisms in a category. In this analogy the object 1 is viewed as a single wire. We show how the two Frobenius monoids associated to the object 2 relate to placing pairs of wires into series and parallel connections. (Received July 06, 2017)

2) Kenny and Daniel have finished writing a paper and put it on the arXiv.

* [Bicategories of spans and cospans](https://arxiv.org/abs/1707.02098v1)

> **Abstract.** If C is a category with chosen pullbacks and a terminal object then, using a result of Shulman, we obtain a fully dualizable and symmetric monoidal bicategory Sp(Sp(C))} whose objects are those of C whose morphisms are spans in C, and whose 2-morphisms

are isomorphism classes of spans of spans in C. If C is a topos, the first author has previously constructed a bicategory MonicSp(Csp(C)) whose objects are those of C, whose morphisms are cospans in C, and whose 2-morphisms are isomorphism classes of spans of cospans in C with monic legs. We prove this bicategory is also symmetric monoidal and even compact closed. We discuss applications of such bicategories to graph rewriting as well as to Morton and Vicary's combinatorial approach to Khovanov's categorified Heisenberg algebra.

3) At the end of my trip to Europe I spent a week in Turin at the Institute for Scientific Interchange. This is a research institute with about 56 scientists run by Mario Rasetti, a physicist who used to do statistical mechanics at the Institute for Advanced Studies. 30 years ago he went back to Italy to set up a roughly similar institute in his home town. They study complex networks and data science.

He's been reading our work and liking it. He asked me to set up a mathematics group there!

If I do this, I'll be hiring a number of postdocs to work on networks, applied category theory and the like. That could be some of you - though of course I don't want to hire just my own students; I want to hire the best people I can find. There should also be opportunities for shorter visits, like conferences and workshops, which some of you might attend.

If I do this I won't be giving up my position at UCR, at least not soon. Instead, I'll visit the place repeatedly, for example during summers. Turin is a wonderful city, so I like this idea. But mainly I'm excited at the idea of being able to put together a team of people working on the kinds of math I like.

It's not 100% certain this will happen: I need to decide I really want to do it, and write a proposal, which the board of the ISI will then read, etc.