Complex mathematical models of data

Real-world systems—from academic collaborations and computer networks to biological systems and power grids—are often large, heterogeneous, and highly interconnected. A first step towards understanding these systems is choosing an appropriate mathematical model. At Pacific Northwest National Laboratory, we model such systems using graphs, hypergraphs, geometric and topological frameworks. In this talk I will give a broad overview of these representations of complex data, how we analyze these models to gain new insights, and how we use those insights to impact real-world domains. I will also discuss how these mathematical structures interface with modern machine learning methods.