Many processes in the life sciences are inherently multi-scale and dynamic. Spatial structures and patterns vary across levels of organisation, from molecular to multi-cellular to multi-organism. With more sophisticated mechanistic models and data available, quantitative tools are needed to study their evolution in space and time. Topological data analysis (TDA) provides a multi-scale summary of data.

We review the main tools in topological data analysis and how single and multi-parameter persistent homology provide insights to biological systems.

Heather Harrington is an MPI Director and Professor of Mathematics. She leads the Algebraic Systems Biology group, which combines algebra, geometry, topology, combinatorics with dynamical systems and biological data. Her research is devoted to developing new mathematical theory and methodologies to solve real-world problems arising in the biological, life and medical sciences.

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