Workshop

Suggested reading

Publications

1. Giordano, Paolo. A mathematical definition of complex adaptive system as interaction space. (https://arxiv.org/abs/2407.02181) 

2. Giordano, Paolo. Interaction spaces: Towards a Universal Mathematical Theory of Complex Systems. (https://arxiv.org/abs/2407.02175v1)

Lecture notes

Here is the list of titles of the lectures of the "Introduction to complex systems" online course by Paolo Giordano that may be related to the workshop.

Lecture 1: Introduction to the Study of Complexity, Properties Common to Complex Systems  (link video 1)

Lecture 2: Core Goals Disciplines and Methodology of the science of complexity, Definitions of Complexity (link video 2)

Lecture 3, 4, 5: What are Complex Systems, Celluar automata, urban parcels (link video 3, link video 4, link video 5)

Lecture 6: Collaborative lectures, White-Engelen model (link video 6)

Lecture 7: White-Engelen model, Calibration, validation and support decisions (link video 7)

Lecture 8: Agent based models 1 (link video 8)

Lecture 9: Agent based models 2 (link video 9)

Lecture 10: Cause-effect preserving functors 1 (link video 10)

Lecture 11: Cause-effect preserving functors 2 (link video 11)

Lecture 12: Ideas for ARC-AGI 1 (link video 12)

Lecture 13: Ideas for ARC-AGI 2 (link video 13)

Lecture 14: A first definition of interaction spaces (link video 14)

Lecture 15: Mathematical definition of complex adaptive systems 1 (link video 15)

Lecture 16: Mathematical definition of complex adaptive systems 2 (link video 16)

All the lecture notes and recording are available here.  

Additional Reference 

1. Chollet, F. et. all. ARC-AGI-2: A New Challenge for Frontier AI Reasoning Systems. 2025 (https://arxiv.org/abs/2505.11831v1) 

2. Modeling Complex Systems (https://link.springer.com/book/10.1007/978-1-4419-6562-2)

3. ⁠⁠Casti, J.L. Would-be worlds: Toward a theory of complex systems. Artificial Life and Robotics 1, 11–13 (1997). https://doi.org/10.1007/BF02471105 

4. CausaLens. An Overview of the Methodologies of Causal Discovery (https://causalai.causalens.com/resources/research/an-overview-of-the-methodologies-of-causal-discovery/) 

5. Ceccherini-Silberstein, Tullio. Michel Coornaert. Springer Monograph in Mathematics: Cellular Automata and Groups. 2010.

6. Dominique Chu, Roger Strand, and Ragnar Fjelland. Theories of Complexity: Common Denominators of Complex Systems. 2003

7. Crutchfield, James P. Between order and chaos. Macmillan Publishers Limited: Nature Physics. 2012. DOI: 10.1038/NPHYS2190

8. Feng, Song. et. all. Hypergraph models of biological networks to identify genes critical to pathogenic viral response. BMC Bioinformatics. https://doi.org/10.1186/s12859-021-04197-2

9. Grothendieck. L’importance d’être seul. 

10. Judea Pearl, AI, and Causality: What Role do Statisticians Play? Amstat News, AI Special Issue, 555:6-9, September 2023. 

11. Leinser, Tom. Basic Category Theory. 2014. Cambridge. 

12. Leinser, Tom. Higher Operads, Higher Categories. http://arXiv.org/abs/math/0305049v1 

13. Llyod, Seth. Measures of Complexity: A Nonexhaustive List. 2001. IEEE Control Systems Magazine. 

14. Kai Nagel, Michael Schreckenberg. A cellular automaton model for freeway traffic. Journal de Physique I, EDP Sciences, 1992, 2 (12), pp.2221-2229. 10.1051/jp1:1992277. jpa- 00246697.