Nagy Kinga: On the h-vector of random simplicial complexes

Consider a random graph where vertices are points in d-dimensional Euclidean space given by a Poisson point process, and the edges are the pairs of vertices whose distance is at most some fixed threshold.
This construction, called the Gilbert graph or random geometric graph, is well-studied in both graph theoretical and geometric settings, with a particular area of interest being subgraph counts, that is, the number of subgraphs isomorphic to an arbitrary fixed graph.
In this talk, we examine random simplicial complexes that are closely related to random geometric graphs.
Specifically, we discuss results regarding the dimension and h-vector of these complexes.