Infrageometry talks in Srní and Madrid

One of the projects I am developing at the Wolfram Institute is Infrageometry: a version of discrete geometry designed as a backbone for the Wolfram Physics Project. Instead of discretizing smooth geometry, the approach goes in the opposite direction. It asks how an observer living on a discrete, indivisible substrate would perceive geometry, and how such perception evolves and branches as the underlying structure is refined.

Concretely, we build minimal models of geometric phenomena on graphs and hypergraphs and study the evolution of observables under hypergraph rewriting. We explore these models across different rules (ruliology), across different branches of multiway evolution (non-determinism), and in the limit of many updates (emergence). By effectively running our own computational universe, we revisit the timeless question of how simple systems give rise to complex behavior that resembles smooth geometry. A concrete mathematical incarnation of this would be generating solutions of PDEs through rewriting.

Beyond minimal models, we aim to constrain rule dynamics through variational principles and to formalize emergent structure via probabilistic and ergodic limit theorems, ultimately seeking to account for fundamental parameters of the universe using only simple, or even no, assumptions at all.

Srní and Madrid

After joining the Wolfram Institute half a year ago, I recently gave my first two talks: one at the 46th Winter School Geometry and Physics in Srní, and one at From Geometric Ideas to Computational Frontiers in Madrid.

Srní is a place I return to regularly. There is a stable core of scientists from the Czech Republic, whom I’ve gotten to know over the years, together with interesting international visitors, mathematicians and mathematical physist. The hotel has all‑you‑can‑eat Czech dinners, a free swimming pool and sauna, and one can go cross‑country skiing or see wolves in the nearby reservation.

The Madrid event came from an invitation by Eva Miranda’s group to explore potential collaboration with the Wolfram Institute on computation in dynamics (this Wolfram Summer School project is an early example). It was an excellent meeting, and I hope it will lead to more joint projects.

Slides

Both talks cover essentially the same material. The Madrid version is a bit more extended in content but includes less code (which does not run anyway without the underlying libraries, currently under construction).

The next major event is the Wolfram Models Conference in Austin (April 17–19), which we organize with support from the John Templeton Foundation.