The process of organism development leads to the emergence of a fully formed organism starting from a single cell, representing one of Nature’s most astonishing phenomena. As development unfolds, numerous processes intricately overlap to construct a viable individual, with its immense complexity —be it a fly, a mouse, or a human being— in a remarkably short amount of time. In this course we will revise several aspects of this intriguing subject following the timeline of embryo development:

–General overview of the early embryo development in animals
–Feedbacks between cell properties, stochasticity, mechanics and topology
–Dynamical singularities in the early embryo dynamics
–Phase transitions in embryonic tissue dynamics
–Phase transitions and symmetry breaking at the onset of morphogenesis

1 Cities, city delineation, Zipf, Gibrat, and migration between cities

2 Scaling

3 The structure of a city

4 Urban mobility

5 Urban violence

– Exponential Dynamics and Limits to Natural-resources Production

– Entropy and the Economic Process

– Environmental Limits: A Dynamic Ecological Perspective

– Agent-based numerical models: World2 (“Limits to Growth”) and Later Models

– Is Collapse Avoidable? An Anthropology and a Systems Perspective on Collapses Throughout History

Many cancers resist therapeutic intervention. This is fundamentally related to intratumor heterogeneity: like species in an ecosystem, multiple cancer populations with different phenotypic signatures coexist inside a tumor. In this brief talk I will present recent methods from theoretical ecology that could help us better understand the complexity of heterogeneous tumors. I will also discuss the interaction between cancer and two other complex systems, the immune system and the gut microbiome, with implications across a wide range of diseases. The goal is to propose open questions and a potential roadmap for further research in cancer, immune and microbial ecology.

The path to the origin of life on Earth was marked by successive transitions toward complexity, from astrochemistry to biomolecules and, eventually, to living organisms. Unraveling the nature of these transitions remains a central challenge in astrobiology, where the potential of complexity theory has yet to be fully realized.

In this seminar, I will first address the main unresolved difficulties in the study of the origin and early evolution of life, and explore how complexity science, in synergy with recent advances in data science, can play a pivotal role in tackling them.

Second, I will focus on the starting point of the long path toward life: the emergence of molecular complexity in outer space. Astrochemistry has undergone dizzying advances over the last decade thanks to large astrophysical facilities such as ALMA and the recently launched James Webb Space Telescope. To date, around 350 molecules have been detected in the interstellar medium, some of prebiotic relevance, and many more are expected in the years ahead. I will explain how we examined the emergence of molecular complexity in space through the lens of network science [1], suggesting that the apparent success of modern astrochemical models in reproducing astrophysical observations may stem less from their fidelity to the real underlying chemical processes than from their excessive complexity and sloppy nature [2,3]. This perspective invites a necessary rethinking of the numerical and formal approaches of this rapidly evolving discipline, highlighting the still uncertain but promising role that complexity theory may play in addressing this challenge.

[1] M. García-Sánchez, I. Jiménez-Serra, F. Puente-Sánchez, J. Aguirre, The emergence of interstellar molecular complexity explained by interacting networks, PNAS 119 (30), e2119734119 (2022).

[2] M. Fernández-Ruz, I. Jiménez-Serra, M. Castro, M. Ruiz-Bermejo and J. Aguirre, Strong parameter hierarchy in the interstellar phosphorus chemical network, Frontiers in Astronomy and Space Sciences 12, 1570525 (2025).

[3] M. Fernández-Ruz, I. Jiménez-Serra and J. Aguirre, A theoretical approach to the complex chemical evolution of phosphorus in the interstellar medium, Astrophysical Journal 956, 47 (2023).

The perfect ‘prescription’: the use of mathematical modelling in pharma

Did you know that for a new drug to be approved by the relevant regulatory agencies, a mathematical model using patient data needs to be developed? Have you ever wondered why certain drugs have different doses depending on individuals’ body weight? In this talk, I will aim to review some of the mathematical modelling work happening behind the scenes in the pharmaceutical industry, as well as sharing some insights based on personal experience on how a theoretical background fits in an industry context.

I hope that, by the end of the talk, you all feel that you were administered the right (content) dose to meet your expectations!