From Geometric Ideas to Computational Frontiers

This event marks the first formal collaboration of the AQUACELL research group with the Wolfram Institute, opening a dialogue between two communities united by a shared fascination with complexity, structure, and computation. Conceived under the theme Ideas in Motion, the activity explores the powerful synergies that emerge when the geometric viewpoint meets the computational paradigm.

As the closing activity of the COMPLEXFLUIDS project financed by the BBVA Foundation, the workshop highlights how geometric insight, dynamical modelling, and algorithmic thinking converge to illuminate complex phenomena from fluid dynamics and celestial mechanics to emergent computation in physical systems.

Bringing together researchers from both institutions, the event aims not only to present recent breakthroughs but also to lay the groundwork for sustained collaboration, bridging mathematical theory, scientific computation, and the broader landscape of complex systems. It represents a launch point for new joint endeavours where ideas flow, interact, and evolve into novel research frontiers.

Venue: Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid

Pl. de las Ciencias, 3, Moncloa - Aravaca, 28040 Madrid, Spain

Aula Miguel de Guzmán

Schedule

11:30 – 12:00

Opening Dean of the UCM and the AQUACELL team

Welcome Remarks and Presentation of the Wolfram Institute:

Introducing the Wolfram Institute

Dugan Hammock (Austin, US)

The Wolfram Research Institute: Vision, Structure, and Mission

12.00-12:30 Coffee break

Session I — Scientific Talks (Chair Daniel Peralta Salas)

12.30- 12.55

Carlos Zapata-Carratalá (Wolfram Institute, Madrid, Spain)

Hypergraphs, Infrageometry and Algebra: a glimpse into a new mathematical realm 

13:10 – 14:00

Outreach Lecture (Chair Daniel Peralta Salas)

Professor Andrzej Żuk (Université de Paris)

Automata in analysis and group theory

14:30-16:00 Lunch

Session II —  The Wolfram Institute Ideas in Motion (Chair Ángel González Prieto)

16:00 – 16:25

Pedro Márquez-Zacarias (Wolfram Institute, Santa Fe, US)

Irreducible complexity in living systems

16:30 – 16:55

Pavel Hajek (Wolfram Institute, Hamburg, Germany)

Infrageometry: Geometry Emerging from Hypergraph Rewriting"

17:00 – 17:30

Isaac Ramos (ETHZ)

Is a Billiard Table the Simplest Universal Physical Computer?

17:30 – 18:00

Open Q&A and Collective Reflections

Concluding Discussion

All participants

Reflections, Future Collaborations, and Plans for the Barcelona Institutional Event

Session III —  The Wolfram Institute Ideas in Motion (Chair Eva Miranda)

18.00-19.00 

Chair: Eva Miranda

Stephen Wolfram, online presentation

What the Universe Can and Cannot Compute

20:30 – 22:30  Conference Dinner