Miguel O’Malley (10/19/2022): Alpha Magnitude

Title: Alpha Magnitude

Abstract: Magnitude is an isometric invariant for metric spaces that was introduced by Leinster around 2010, and is currently the object of intense research, since it has been shown to encode many known invariants of metric spaces. In recent work, Govc and Hepworth introduced persistent magnitude, a numerical invariant of a filtered simplicial complex associated to a metric space. Inspired by Govc and Hepworth’s definition, in this talk the definition of alpha magnitude will be introduced, along with some of its key properties. Heuristic observations and a following conjecture regarding a relationship with the Minkowski dimension of compact subspaces of Euclidean space will be shown. Alpha magnitude presents computational advantages over both magnitude as well as Rips magnitude, and we thus propose it as a new measure for the estimation of fractal dimensions of real-world data sets that is easily computable.