From the Organizer:

Complex networks are a popular means for studying a wide variety of systems across the social and natural sciences and, more recently, representing big data. Recent technological advances allow for a description of these systems on an unprecedented scale. However, due to the immense size and complexity of the resulting networks, efficient evaluation remains a data-analytic challenge.

In a recent series of articles [Weber, Saucan, Jost; J. Complex Networks 2017, 2018], Melanie Weber and her team developed geometric tools for efficiently analyzing the structure and evolution of complex networks. The core component of their theory, a discrete Ricci curvature, translates central tools from differential geometry to the discrete realm. With these tools, they extend the commonly used node-based approach to include edge-based information such as edge weights and directionality for a more comprehensive network characterization. The analysis of a wide range of complex networks suggests connections between curvature and higher order network structure. Their results identify important structural features, including long-range connections of high curvature acting as bridges between major network components. Curvature-based tools allow for an efficient computation of this core structure and, based on this core structure, more expensive analysis, hypothesis testing and learning of complex models becomes more feasible.


About our speaker:
Melanie Weber is a Ph.D. student at Princeton with an undergraduate degree in math and physics from the University of Leipzig in Germany (where she hails from). Her research interests include (non-Euclidean) geometry and functional analysis, and its applications in machine learning and optimization.

Melanie's Princeton profile:
https://web.math.princeton.edu/~mw25/