## January 24, 2021

### Open Systems: A Double Categorical Perspective (Part 3)

#### Posted by John Baez

Back to Kenny Courser’s thesis:

- Kenny Courser,
*Open Systems: A Double Categorical Perspective*, Ph.D. thesis, U. C. Riverside, 2020.

Last time I explained the problems with decorated cospans as a framework for dealing with open systems. I vaguely hinted that Kenny’s thesis presents *two* solutions to these problems: so-called ‘structured cospans’, and a new improved approach to decorated cospans. Now let me explain these!

## January 20, 2021

### Postdoctoral Position in HoTT at the University of San Diego

#### Posted by Mike Shulman

The University of San Diego invites applications for a postdoctoral research fellowship in homotopy type theory beginning Fall 2021, or earlier if desired. This is intended as a two-year position with potential extension to a third year, funded by the second AFOSR MURI grant for HoTT, entitled “Synthetic and Constructive Mathematics of Higher Structures in Homotopy Type Theory”.

## January 19, 2021

### Categories of Nets (Part 2)

#### Posted by Mike Shulman

Now that John gave an overview of the Petri nets paper that he and I have just written with Jade and Fabrizio, I want to dive a bit more into what we accomplish. The genesis of this paper was a paper written by Fabrizio and several other folks entitled Computational Petri Nets: Adjunctions Considered Harmful, which of course sounds to a category theorist like a challenge. Our paper, and particularly the notion of $\Sigma$-net and the adjunction in the middle column relating $\Sigma$-nets to symmetric strict monoidal categories, is an answer to that challenge.

## January 17, 2021

### Categories of Nets (Part 1)

#### Posted by John Baez

I’ve been thinking about Petri nets a lot. Around 2010, I got excited about using them to describe chemical reactions, population dynamics and more, using ideas taken from quantum physics. Then I started working with my student Blake Pollard on ‘open’ Petri nets, which you can glue together to form larger Petri nets. Blake and I focused on their applications to chemistry, but later my student Jade Master and I applied them to computer science and brought in some new math. I was delighted when Evan Patterson and Micah Halter used all this math, along with ideas of Joachim Kock, to develop software for rapidly assembling models of COVID-19.

Now I’m happy to announce that Jade and I have teamed up with Fabrizio Genovese and Mike Shulman to straighten out a lot of mysteries concerning Petri nets and their variants:

- John Baez, Fabrizio Genovese, Jade Master and Mike Shulman, Categories of nets.

This paper is full of interesting ideas, but I’ll just tell you the basic framework.

## January 12, 2021

### This Week’s Finds (1–50)

#### Posted by John Baez

Take a copy of this!

• *This Week’s Finds in Mathematical Physics (1-50)*, 242 pages.

These are the first 50 issues of *This Week’s Finds of Mathematical Physics*. This series has sometimes been called the world’s first blog, though it was originally posted on a “usenet newsgroup” called sci.physics.research — a form of communication that predated the world-wide web. I began writing this series as a way to talk about papers I was reading and writing, and in the first 50 issues I stuck closely to this format. These issues focus rather tightly on quantum gravity, topological quantum field theory, knot theory, and applications of *n*-categories to these subjects. There are, however, digressions into elliptic curves, Lie algebras, linear logic and various other topics.

## January 3, 2021

### Postdoctoral Position in HoTT at Johns Hopkins University

#### Posted by Emily Riehl

The Department of Mathematics at Johns Hopkins University solicits applications for one two-year postdoctoral fellowship beginning Summer 2021 (with some flexibility in the start and end dates). The position is funded by the Air Force Office of Scientific Research (AFOSR) through the Multidisciplinary University Research Initiative (MURI) program. This position is open to anyone who is able to obtain a visa to come and work in the US, but it is necessary to be physically in the US to receive funding from this grant. (Johns Hopkins will sponsor and pay for a visa application, if required.)

The $n$-Category Café has recently hosted a lively discussion on the ethics of military funded mathematics and US military funding in particular. This is the first time I’ve collaborated on a military funded grant, so I have limited experience in this area. But every year, I’m heartbroken to disappoint the dozens of highly-qualified postdoctoral applicants I come in contact with. My department also offers university-funded postdoctoral positions (though one could argue that military funding provides some support for all employees at Johns Hopkins) but at some point I calculated that it would be “my turn” to make an offer to my first choice candidate exactly once a decade, and I wanted to try to find a way to hire others in the meanwhile.

## January 2, 2021

### Applied Category Theory 2021 Adjoint School

#### Posted by John Baez

Do you want to get involved in applied category theory? Are you willing to do a lot of work and learn a lot? Then this is for you:

- Applied Category Theory 2021 – Adjoint School. Applications due Friday 29 January 2021. Organized by David Jaz Myers, Sophie Libkind, and Brendan Fong.

There are four projects to choose from, with great mentors. You can see descriptions of them below!

By the way, it’s not yet clear if there will be an in-person component to this school — but if there is, it’ll happen at the University of Cambridge. ACT2021 is being organized by Jamie Vicary, who teaches in the computer science department there.