Selected Research Projects

Expert Detection via Sheaf Laplacian

This project introduces a sheaf-theoretic framework for identifying domain experts in complex, multi-layered networks such as crowdsourcing forums and healthcare collaboration systems. By encoding user attributes, interaction patterns, and contextual dependencies as data attached to a network sheaf, we build a Sheaf Laplacian whose diffusion dynamics reveal both local consistency and global expertise signals. Unlike traditional graph-based methods that rely solely on structural connectivity, the sheaf Laplacian integrates semantic information—such as topic alignment, communication quality, and task performance—to more accurately distinguish genuine expertise from mere activity. Applied to large crowdsourcing platforms and clinical collaboration networks, this approach uncovers hidden expert communities, improves task routing, and supports more trustworthy decision-making in real-world settings.

Persistent Homology of Networks

This project uses topological ideas to uncover hidden structural patterns in complex networks, from healthcare systems to higher-order relational data. In our work with electronic health records, we extract multi-scale connectivity patterns from patient–provider interaction networks to improve the prediction of critical outcomes in intensive care units. In parallel, we develop topology-based representations for hypergraphs that capture higher-order relationships beyond pairwise connections. Across both efforts, we show that understanding the “shape” of network data provides information that traditional graph or machine-learning models overlook, leading to better classification and outcome prediction in real-world settings.

Influential node and higher-order interactions detection on networks.

Identifying influential nodes in a complex network is an important graph mining problem with many diverse applications such as information propagation, market advertising, and rumor controlling. Influential nodes in a network play critical roles and largely affect network structure and functions more than the rest of the network. They are able to diffuse or spread information throughout a complex network more rapidly. In this project, we detect the important nodes and higher-order interactions in networks that have key roles in information diffusion.  

Modeling diffusion on Hypergraphs.

Diffusion on networks is an important concept in network science that models how a stuff, such as information and heat, diffuses between vertices based on network topology, the pattern of who is connected to whom. In this project, we develop new hypergraph Laplacians to model diffusion more comprehensively.