Path signatures in topology, dynamics and data analysis

The signature of a path in Euclidean space resides in the tensor algebra of that space; it is obtained by systematic iterated integration of the components of the given path against one another. This straightforward definition conceals a host of deep theoretical properties and impressive practical consequences. In this talk I will describe the homotopical origins of path signatures, their subsequent application to stochastic analysis, and how they facilitate efficient machine learning in topological data analysis. This last bit is joint work with Ilya Chevyrev and Harald Oberhauser. 

About the speaker

Dr Nanda develops algebraic-topological theories, algorithms and software for the analysis of non-linear data and complex systems arising in various scientific contexts. In particular, he employs discrete Morse-theoretic techniques to substantially compress cell complexes built around the input data without modifying core topological properties.

His recent work has involved excursions into computational geometry, cellular sheaf theory and higher-categorical localization.