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DSOFT/GSNP Short Course: Introduction to Topological Data Analysis

DSOFT/GSNP Short Course: Introduction to Topological Data Analysis

Algebraic topology gives a framework to rigorously and quantitatively describe the global structure of a space, and the idea of \emph{topological data analysis} (TDA) allows one to do this with empirical data (from either models or experiments), rather than simply with abstract mathematical spaces. TDA is becoming increasingly accessible, which one can see in the explosion of research on it, with many contributions in physics and from the physics community. Applications of TDA are diverse and expanding rapidly, including to many physical systems, with prominent research efforts in topics like granular materials, swarming of particles (such as in the famous Vicsek model), the biophysics of lead-venation patterns, activation patterns in the brain, and many more.