CERAMATHS - DMATHS seminar: presentation by Tom Garcia-Sanchez

The CÉRAMATHS mathematics department seminar will welcome Tom Garcia-Sanchez (IMT Nord Europe) at 2pm, Thursday December 11, 2025, for the following talk:

The infinite branches of the Radial Spanning Tree

The Radial Spanning Tree is a geometric graph defined by a simple, deterministic local rule on a random infinite set of points in Euclidean space. It forms almost surely a locally finite rooted tree, prompting several natural questions: How many infinite branches are there? Do they admit asymptotic directions? Which limits are possible? How many distinct infinite branches can share the same one? In this talk, we will review how these questions were addressed in the two-dimensional case. Then, we will present recent progress that makes it possible to investigate higher dimensions, where previous approaches failed due to the loss of planarity.