There’s a ‘school’ on applied category theory one week before the workshop Applied Category Theory 2018. The deadline for applying to this school is Wednesday November 1st.

• Applied Category Theory: Adjoint School: online sessions starting in January 2018, followed by a meeting 23–27 April 2018 at the Lorentz Center in Leiden, the Netherlands. Organized by Bob Coecke (Oxford), Brendan Fong (MIT), Aleks Kissinger (Nijmegen), Martha Lewis (Amsterdam), and Joshua Tan (Oxford).

The name ‘adjoint school’ is a bad pun, but the school should be great. Here’s how it works:

### Overview

The Workshop on Applied Category Theory 2018 takes place in May 2018. A principal goal of this workshop is to bring early career researchers into the applied category theory community. Towards this goal, we are organising the Adjoint School.

The Adjoint School will run from January to April 2018. By the end of the school, each participant will:

- be familiar with the language, goals, and methods of four prominent, current research directions in applied category theory;
- have worked intensively on one of these research directions, mentored by an expert in the field; and
- know other early career researchers interested in applied category theory.

They will then attend the main workshop, well equipped to take part in discussions across the diversity of applied category theory.

### Structure

The Adjoint School comprises (1) an Online Reading Seminar from January to April 2018, and (2) a four day Research Week held at the Lorentz Center, Leiden, The Netherlands, from Monday April 23rd to Thursday April 26th.

In the Online Reading Seminar we will read papers on current research directions in applied category theory. The seminar will consist of eight iterations of a two week block. Each block will have one paper as assigned reading, two participants as co-leaders, and three phases:

- A presentation (over WebEx) on the assigned reading delivered by the two block co-leaders.
- Reading responses and discussion on a private forum, facilitated by Brendan Fong and Nina Otter.
- Publication of a blog post on the
*n*-Category Café written by the co-leaders.

Each participant will be expected to co-lead one block.

The Adjoint School is taught by mentors John Baez, Aleks Kissinger, Martha Lewis, and Pawel Sobocinski. Each mentor will mentor a working group comprising four participants. During the second half of the Online Reading Seminar, these working groups will begin to meet with their mentor (again over video conference) to learn about open research problems related to their reading.

In late April, the participants and the mentors will convene for a four day Research Week at the Lorentz Center. After opening lectures by the mentors, the Research Week will be devoted to collaboration within the working groups. Morning and evening reporting sessions will keep the whole school informed of the research developments of each group.

The following week, participants will attend Applied Category Theory 2018, a discussion-based 60-attendee workshop at the Lorentz Center. Here they will have the chance to meet senior members across the applied category theory community and learn about ongoing research, as well as industry applications.

Following the school, successful working groups will be invited to contribute to a new, to be launched, CUP book series.

### Reading list

Meetings will be on Mondays; we will determine a time depending on the locations of the chosen participants.

- Jan 8: B. Coecke, M. Sadrzadeh, and S. Clark, Mathematical foundations for a compositional distributional model of meaning,
*Linguistic Analysis***36**(2010), 345–384. - Jan 22: A. Kissinger and S. Uijlen. A categorical semantics for causal structure,
*32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)*2017, pp. 1-12 - Feb 5: B. Fong, Decorated cospans,
*Theory and Applications of Categories***30**(2015), 1096–1120. - Feb 19: A. Carboni and R.F.C. Walters. Cartesian bicategories I,
*Journal of Pure and Applied Algebra***49**(1987), 11–32. - Mar 5: J. Bolt, B. Coecke, F. Genovese, M. Lewis, D. Marsden, and R. Piedeleu.
*Interacting conceptual spaces I: grammatical composition of concepts*, arXiv preprint, 2017. - Mar 19: J. Baez and B. Pollard, A compositional framework for reaction networks,
*Reviews in Mathematical Physics***29**(2017), 1750028. - Apr 2: J.C. Willems, The behavioral approach to open and interconnected systems,
*IEEE Control Systems***27**(2007), 46–99. - Apr 16: J. Henson, R. Lal, and M. Pusey, Theory-independent limits on correlations from generalised Bayesian networks,
*New Journal of Physics***27**(2014), 113043.

### Research projects

**John Baez: Semantics for open Petri nets and reaction networks**

Petri nets and reaction networks are widely used to describe systems of interacting entities in computer science, chemistry and other fields, but the study of open Petri nets and reaction networks is new, and raise many new questions connected to Lawvere’s “functorial semantics”.

*Reading: Fong; Baez and Pollard.*

**Aleks Kissinger: Unification of the logic of causality**

Employ the framework of (pre-)causal categories to unite notions of causality and techniques for causal reasoning which occur in classical statistics, quantum foundations, and beyond.

*Reading: Kissinger and Uijlen; Henson, Lal, and Pusey.*

**Martha Lewis: Compositional approaches to linguistics and cognition**

Use compact closed categories to integrate compositional models of meaning with distributed, geometric, and other meaning representations in linguistics and cognitive science.

*Reading: Coecke, Sadrzadeh, and Clark; Bolt, Coecke, Genovese, Lewis, Marsden, and Piedeleu.*

**Pawel Sobocinski: Modelling of open and interconnected systems**

Use Carboni and Walters’ bicategories of relations as a multidisciplinary algebra of open and interconnected systems.

*Reading: Carboni and Walters; Willems.*

### Applications

We hope that each working group will comprise both participants who specialise in category theory and in the relevant application field. As a prerequisite, those participants specialising in category theory should feel comfortable with the material found in Categories for the Working Mathematician or its equivalent; those specialising in applications should have a similar graduate-level introduction.

To apply, please fill out the form here. You will be asked to upload a single PDF file containing the following information:

- Your contact information and educational history.
- A brief paragraph explaining your interest in this course.
- A paragraph or two describing one of your favorite topics in category theory, or your application field.
- A ranked list of the papers you would most like to present, together with an explanation of your preferences. Note that the paper you present determines which working group you will join.

You may add your CV if you wish.

Anyone is welcome to apply, although preference may be given to current graduate students and postdocs. Women and members of other underrepresented groups within applied category theory are particularly encouraged to apply.

Some support will be available to help with the costs (flights, accommodation, food, childcare) of attending the Research Week and the Workshop on Applied Category Theory; please indicate in your application if you would like to be considered for such support.

If you have any questions, please feel free to contact Brendan Fong (bfo at mit dot edu) or Nina Otter (otter at maths dot ox dot ac dot uk).

Application deadline: **November 1st, 2017.**

Here’s the schedule for the ACT 2018 Adjoint School:

The Adjoint School of Applied Category Theory 2018 is done! Four mentors – Aleks Kissinger, Pawel Sobocinski, Martha Lewis and myself – worked with teams of students to solve problems on causality, linear dynamical systems, linguistics and biology, respectively.

My team, from left to right here, consisted of Blake Pollard working on power grids at NIST, Maru Saruzola doing algebraic K-theory at Cornell, Fabrizio Genovese working in Bob Coecke’s quantum group in computer science at Oxford, and Jonathan Lorand doing symplectic geometry in a postdoc in Zurich:

We discovered some surprising results about the math of ATP coupling, and now we need to write them up.

Two more students in the Applied Category Theory 2018 school wrote a blog article about applications of convex sets:

• Tai-Danae Bradley and Brad Theilman, Cognition, convexity and category theory, The

n-Category Café, 10 March 2018.As part of the Applied Category Theory 2018 school, Maru Sarazola wrote a blog article on open dynamical systems and their steady states. Check it out:

• Maru Sarazola, Dynamical systems and their steady states, 2 April 2018.

She compares two papers:

• David Spivak, The steady states of coupled dynamical systems compose according to matrix arithmetic.

• John Baez and Blake Pollard, A compositional framework for reaction networks,

Reviews in Mathematical Physics29(2017), 1750028.(Blog article here.)

Two more students in the Applied Category Theory 2018 school wrote a blog article about something they read:

• Eliana Lorch and Joshua Tan, The behavioral approach to systems theory, 15 June 2018.

Eliana Lorch is a mathematician based in San Francisco. Joshua Tan is a grad student in computer science at the University of Oxford and one of the organizers of Applied Category Theory 2018.

They wrote a great summary of this paper, which has been an inspiration to me and many others:

• Jan Willems, The behavioral approach to open and interconnected systems,

IEEE Control Systems27(2007), 46–99.