Seminario Álgebra Geometría Algebraica y Aritmética
Automorphisms of the Rado meet-tree
Ponente: Arturo Rodríguez Fanlo (UAM)Fecha: lunes 20 de octubre de 2025 - 11:00Lugar: Aula 420, Módulo 17, Departamento de Matemáticas, UAM
Resumen:
Oligomorphic groups naturally arise as the groups of automorphisms of universal structures. One of the most basic problems in the study of these groups is computing their normal subgroups. Well-known examples include the group of infinite countable permutations, which has two non-trivial normal subgroups, the group of order-preserving bijections of the rationals, which has three non-trivial normal subgroups, and the Galois group of the complex numbers over the algebraic numbers, which is simple. Unlike most classical examples of oligomorphic groups, which are simple or have very few normal subgroups, the group of automorphisms of the universal (meet-)tree has a continuum of normal subgroups. However, this apparent complexity disappears if one imposes a randomness-preserving condition on the automorphisms. In this talk, we will prove that the group of automorphisms of the Rado meet-tree is simple.
