**1st November 2017**.

- John Baez –
*Semantics for open Petri nets and reaction networks* - Aleks Kissinger –
*Unification of the logic of causality* - Martha Lewis –
*Compositional approaches to linguistics and cognition* - Pawel Sobocinski –
*Modelling of open and interconnected systems*

- A Carboni and RFC Walters.
*Cartesian bicategories I*. Journal of pure and applied algebra 49.1-2 (1987): 11-32. - JC Willems.
*The behavioral approach to open and interconnected systems*. IEEE Control Systems 27.6 (2007): 46-99.

The data revolution of recent years means that scientific models (in physics, biology, medicine, chemistry, climate science, computer science, systems theory, …) are getting larger, more fine-grained and detailed and ever more complex. Algorithms that answer questions about model behaviour are often exponentional in the size of the model, meaning that–even with advances in hardware and software parallelisation–studyingmonolithicmodels usually does not scale. Moreover, monolithic models are poor engineering practice; for example, they are not portable in the sense that standard components cannot be reused from one application to another. These are just some of the reasons why acomprehensive mathematical theory of open and interconnected systems is urgently needed.

As Willems argued inThe behavioral approach to open and interconnected systems, models for such systems must be fundamentally relational in order to be useful – the underlying physical equations that govern behaviour (e.g. Ohm’s law, the gas laws, …) are seldom causal: they merely govern the relationship between various system variables. This contrasts with the human custom of thinking causally about system behaviour. Willems argued that causality–while useful for human intuition–is physically dubious, not compositional and often complicates the mathematics.

To arrive at a comprehensive relational theory of open systems, category theory is unavoidable: one needs the generality to cover the wide variety of mathematical universes relevant in the various application areas, while identifying common structure. Carboni and Walters’Cartesian Bicategoriesof relations offers a general and elegant framework for relational theories and has the potential to be relevant across multiple application areas.

- Assemble a menagerie of relational theories from a variety of disciplines
- Evaluate cartesian bicategories of relations as a mathematical foundation of open and interconnected systems
- Study extensions (abelian bicategories, nonlinear variants)

We’re delighted to announce the Applied Category Theory 2018 Adjoint School, an initiative to bring early career researchers into the applied category theory community.

The Adjoint School comprises two phases: (1) an online reading seminar based on the recent Kan Extension Seminars, and (2) a four day research week at the Lorentz Center, Leiden, The Netherlands. Participants will also be invited to attend Applied Category Theory 2018, which will be held immediately following the research week, also at the Lorentz Center.

During the school, participants will work under the mentorship of four mentors, on one of the following research projects:

- John Baez: Semantics for open Petri nets and reaction networks
- Aleks Kissinger: Unification of the logic of causality
- Martha Lewis: Compositional approaches to linguistics and cognition
- Pawel Sobocinski: Modelling of open and interconnected systems
The online seminar begins in early January 2018, and will run until the research week begins on April 23rd, 2018. Applied Category Theory 2018 will be held April 30th to May 4th.

Applications to participate in the school are now open. For more details, including how to apply, please see here:

http://www.appliedcategorytheory.org/school or contact the organisers. Applications close November 1st.

On behalf of the organisers,Brendan Fong (bfo@mit.edu)Nina Otter (otter@maths.ox.ac.uk)