Poisson Point Processes and Random Simplicial Complexes

Point clouds appear naturally in data analysis and machine learning when studying samples or related constructions like persistence homology.

Based on ideas from stochastic geometry, generic behaviour of such clouds can be modelled via point processes and here we focus on the case of Poisson point processes.

In particular, using Vietoris-Rips or $C\v{e}ch$ complexes this yields models for random simplicial complexes. In this talk we discuss recent results from an algebraic and combinatorial perspective.