| Thursday 16 January 2025 | |
| Events for day: Wednesday 31 May 2023 |
| 16:00 - 17:00 Mathematics Colloquium Bootstrap Percolation on Graphs School MATHEMATICS We discuss two notions of percolation on graphs. The first one is $r$-neighbor bootstrap percolation in which an activation process of the vertices of a given graph is carried out. The process starts with some initially activated vertices and then, in each round, any inactive vertex with at least $r$ active neighbors becomes activated. The second one is the so called graph bootstrap percolation in which we activate the edges of a graph instead of vertices. Starting with some initially activated edges, we activate any inactive edge which creates a new copy of $H$, the pattern or base graph. Two problems, one of combinato ... 17:30 - 19:00 Number Theory Webinar Abelian Arboreal Representations School MATHEMATICS I will present joint work with Andrea Ferraguti which makes progress on a conjecture of Andrews and Petsche that classifies abelian dynamical Galois groups over number fields, in the unicritical case. I will explain how to reduce the conjecture to the post-critically finite case and the key tools to handle all unicritical PCF with periodic critical orbit over any number field and all PCF over quadratic number fields. Along the way I will present an earlier rigidity result of ours on the maximal closed subgroup of the automorphism group of a binary rooted tree, which offered us with the main input to translate the commutativity of the Galois i ... |