Sayeh Khaniha

This project develops a new mathematical model for community detection in networks where both hierarchy and geometric shape interactions. Classical stochastic block models describe hidden communities, while geometric random graphs capture the fact that nearby nodes are more likely to connect. Many real systems, however, combine both features: communities are nested across several scales and interactions are constrained by spatial or feature-space proximity. Sayeh Khaniha will study a Geometric Hierarchical Stochastic Block Model, deriving theoretical thresholds for when communities can be recovered and designing efficient algorithms that approach these limits. The project will combine tools from probability, stochastic geometry, information theory, and machine learning. It will also explore applications to biological interaction data, such as RNA-binding protein networks, where spatial locality and multi-scale functional organization coexist. The aim is to provide mathematically rigorous and computationally scalable methods for interpretable network inference in complex high-dimensional data.