Kick-off event: AI and the future of mathematics and physics - 21.10.2026
In light of recent developments, the incoming kick-off event at the Institut Henri Poincaré will take the form of a debate gathering mathematicians and theoretical physicists around the role of AI in the practice of research. Registration: indico.math.cnrs.fr/event/17376/.
Scale-invariant random geometries from mating of trees
byAlicia Castro
Abstract:In this talk, I present new results on the search for scale-invariant random geometries in the context of Quantum Gravity. To uncover new universality classes of such geometries, we generalized the mating of trees approach, which encodes Liouville Quantum Gravity on the 2-sphere in terms of a correlated Brownian motion describing a pair of random trees. We extended this approacyouh to higher-dimensional correlated Brownian motions, leading to a family of non-planar random graphs that belong to new universality classes of scale-invariant random geometries. We developed a numerical method to efficiently simulate these random graphs and explore their scaling limits through distance measurements, allowing us to estimate Hausdorff dimensions in the two- and three-dimensional settings.
Keywords:
Quantum Gravity, Random Geometry