UChicago PME Materials Special Seminar- Victor M. Zavala

Quantifying the Shape of Materials Data using Topology

We discuss how techniques from topology can be used for representing, analyzing, and quantifying the shape of complex datasets. Specifically, we discuss how datasets arising from molecular simulation, microscopy, and chemical processes can be represented in a unified manner as topological objects (graphs/networks, simplicial complexes, and manifolds), how one can quantify the shape of such objects using simple topological descriptors, and how one can use such descriptors for visualizing and predicting emergent phenomena. We provide case studies showcasing how topology can be used for designing chemoresponsive liquid crystals, for linking the microstructure of soft gels to their rheological properties, for understanding how the structure of solvent environments affect liquid-phase reactions, and for detecting events from multivariate time series data. We also discuss how topological analysis provides interpretable results and enables highly scalable computations (compared to machine learning approaches such as convolutional neural networks).