Abstract: Topological data analysis is a relatively new field whose goal is to extract information from data by topological methods. The basic philosophy is that data has an inherent geometry, it has "shape", and this shape carries information that we would like to quantify. The goal is to make this hidden information visible using algebraic topology. In a joint work with S. Kalisnik and V. Limic we put forward some aspects of the probabilistic foundations of the theory in order to make it more useful for statistical applications.
basic topology: topological space, metric space, knowledge of homology is a psychological advantage, but not necessary to be able to follow. (I will briefly explain what I need)
basic algebra: field, group, vector spaces
basic probability theory and analysis: measure, random variable, Banach space, completion