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**Learn applied category theory!**

It's not too late to apply to this school on applied category theory! I'm one of the teachers, and we're still looking for a few more good students - but the deadline to apply is Wednesday November 1st! To apply, go here:

http://www.appliedcategorytheory.org/school/

**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:

https://docs.google.com/forms/d/e/1FAIpQLSfSm-tY9zHi4vuWd2BiyNtu3KaytQLE0PVj3hQ32DIGUQtO9g/viewform

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.

View 8 previous comments

- +Emilio Jesús Gallego Arias - oh! Lots of people are going to the workshop but not the school. However, there is limited space at the workshop, so it may be full. Or maybe not. You can find out.

I'm not one of the organizers, by the way. But I posted an ad for the workshop a while ago, here:50w - That's a very nice setup! I'll see if I can find the time to follow some of the fun happening online. I'm also considering to clear out some more free time and check if I can hop over to Leiden in time to buy you a drink, +John Baez. The workshop looks very appealing as well, but I'd hate to add myself to any crowding, in case that turns out to be the case. I'll check with the organizers when I need to decide, promised :) I can also imagine that you yourself might get pretty busy, in which case I'd gladly prefer to stick with my no-crowding rule, and wait for better times.49w
- +Refurio Anachro - I think it will be good to wait for some better time. I'll be insanely busy at the workshop, since 60 people working on applied category theory will be there, and everyone will be trying to talk to everyone else, trying to develop this new subject.49w
- Sure, thanks for your quick answer, +John Baez! I'm not in a hurry and I am still curious about the whole event. I wonder if someone will record the seminars for the public...49w
- +Refurio Anachro - the plan is to videotape the "workshop" in Leiden (April 30-May 4) and put the videos on OxfordQuantumVideo (see below).

The online part of the "school" will not be videotaped, since it's just 16 students talking to each other about the papers on the reading list, and sometimes a "mentor" helping them work on problems. The students will summarize these papers and put their summaries on the n-Category Cafe for the world to see and discuss. Then they will meet in Leiden (April 23-26) and try to finish solving those problems.

At least I think that's the plan. I'm not one of the organizers, just a "mentor" and a speaker at the workshop.49w - >
*[helpful things] I'm not one of the organizers*

:-D

Yeah, I know, thanks! I have to sleep now.49w

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