Modelling the universe, relative and evolving persistence, and capturing data with bagplots.

Abstract: This lecture will be somewhat of a potpourri of (i) applications of topological concepts, (ii) some quite general statistical methodology for analysing homological characteristics of data sets, and (iii) a probabilistic technique for generating almost independent, identically distributed, realisations of persistence diagrams.

The applications are real, and primarily cosmological. They will be exploited (together with some much simpler toy examples) to demonstrate the new methodologies and the stochastic modelling. In fact, most of the methodologies and models were originally designed for the application, and only afterwards developed as generic tools.

I shall assume that the listeners know what a persistence diagram is, but no other prerequisites are required.

computational geometryalgebraic topologycombinatoricsgeometric topologyprobability

Audience: advanced learners

Asia Pacific Seminar on Applied Topology and Geometry