Topological flow data analysis: how to extract information that matters from flow patterns

Abstract: In many fluid phenomena, experiments and simulations are generating more and more high-resolution time series data, and these pose a problem of great potential usefulness: how can we extract significant, low-dimensional invariants that capture the complexity of any pattern which flows in time?  One approach on the rise is topological flow data analysis (TFDA).  I will explain a reduced-order topological model for mapping a flow evolution to a discrete dynamical system, and illustrate its versatility with an application to echocardiography in the left ventricle of the human heart.