Slawomir Solecki (Cornell)
Title: Simplicial complexes, stellar moves, projective amalgamation, and set theory
Time: Wednesday, 18.06.2025, 14:00.
Place: Renyi, Turan.
Abstract: The talk will explore connections between stellar moves on simplicial complexes (these are fundamental operations of combinatorial topology), amalgamation classes (these classes of structures extensively studied in combinatorics), and projective Fra{\"i}ss{\'e} limits (this is a model theoretic construction with topological applications). We may also touch on relations between these topics and topological dynamics.
The technical core of the talk will consist of identifying a class of simplicial maps that arise from the stellar moves of welding and subdividing. We call these maps weld-division maps. Our main theorem asserts that the category of weld-division maps fulfills the projective amalgamation property. As we will explain, the method of proof of the amalgamation theorem is new. It is not geometric or topological, but rather it consists of combinatorial calculations performed on finite sequences of finite sets. Set theoretic nature of the entries of the sequences is crucial to the arguments.
Jan Grebik (University of Leipzig)
Title: Vanishing uniqueness for Poisson-Voronoi percolation
Time: Wednesday, 19.06.2025, 14:00.
Place: Renyi, Turan.
Abstract: The Poisson−Voronoi percolation model on a locally compact metric space with measure (M,d,μ) is defined as follows. For λ>0, consider a Poisson point process of intensity λμ and associate to each point its Voronoi cell, that is, the set of all points in M closer to this point than to any other point of the Poisson process. For p∈ (0,1), erase each cell with probability p independently of all other cells. This defines a random closed subset ω(λ,p) of M that is the Poisson−Voronoi percolation model with parameters (λ,p). In this talk, I will discuss a recent result with Konstantin Recke that shows that in some spaces the uniqueness thresholds for Poisson-Voronoi percolation converge to zero in the low-intensity limit. This phenomenon is fundamentally different from the situations in which Poisson-Voronoi percolation has previously been studied.