Rachel Skipper: On the Cantor-Bendixson rank of the Grigorchuk group and the Gupta-Sidki 3 group & Hugo Vanneuville: Dynamical Voronoi percolation

Speaker 1: Rachel Skipper

Title: On the Cantor-Bendixson rank of the Grigorchuk group and the Gupta-Sidki 3 group

Abstract: We study the Cantor-Bendixson rank for the space of subgroups of the Grigorchuk group and the Gupta-Sidki group.In particular, we show that for G the Grigorchuk group or the Gupta-Sidki 3 group, the Cantor-Bendixson rank of Sub(G) is $\omega$. This is a joint project with Phillip Wesolek. 

Speaker 2: Hugo Vanneuville

Title: Dynamical Voronoi percolation

Abstract: Consider a Poisson point process in the plane, construct its Voronoi tiling, and colour each tile in black with probability 1/2 and in white with probability 1/2. This defines a critical Voronoi percolation configuration. We prove that, if we let each point move according to a long range stable Lévy process, then there exist atypical (random) times with an unbounded monochromatic component. To this purpose, we study a continuous spectral object - the annealed spectral sample - which is a continuous analogue of the spectral sample studied by Garban, Pete and Schramm.