Research

My research develops mathematical and computational frameworks to analyze complex systems where interactions involve multiple entities simultaneously. By combining topological data analysis, network science, and information theory, I tackle problems in neuroscience and complex systems where traditional pairwise approaches fall short.

Higher-Order Networks & Topology

Complex systems often exhibit interactions that go beyond simple pairwise relationships. I develop mathematical tools to model and analyze these higher-order interactions—relationships involving three or more entities at once. Recent Work:

• The Topology of Synergy (2025) Bridging topological and information-theoretic frameworks to understand synergy in complex systems, revealing how higher-order structures encode emergent information
• Cluster Synchronization via Graph Laplacian (2025) Novel methods for cluster synchronization using graph Laplacian eigenvectors, advancing our understanding of collective dynamics
• XGI Software (2023): Co-developed comprehensive Python package for higher-order network analysis, now widely used in the research community
• Simplicial Configuration Model (2017) A null model for hypothesis testing in higher-order networks that preserves structural properties while randomizing connections
• Networks Beyond Pairwise Interactions (2020) Understanding synchronization and collective behaviors in systems with multi-way interactions Software: XGI - Python package for higher-order networks

Topological Neuroscience & Alzheimer’s Disease

I apply topological and machine learning methods to understand relationships between brain structure, gene expression, and disease progression. My work reveals how mathematical topology can capture biological organization and predict clinical outcomes. Recent Work:

• Integrating Amyloid Imaging and Genetics (2024) Principal Investigator on “Integrative Predictive Modeling of Alzheimer’s Disease” which includes published machine learning framework in Alzheimer’s & Dementia for early disease prediction using multimodal imaging and genetics
• ECoG Analysis (2020) Used persistent homology to detect different level of conscoiusness during anesthesia
• Topological Gene Networks Recapitulate Brain Anatomy (2019) Demonstrated that gene co-expression networks recapitulate known brain anatomy, particularly in the dopaminergic pathway Software: AHBA Microarray Mapper

Sheaf Theory & Information in Complex Systems

Real-world data is inherently noisy and complex systems exhibit emergent synergistic behaviors. My most recent endavour is to develop sheaf-theoretic and information-theoretic frameworks that characterize uncertainty and higher-order information directly into mathematical models. Latest Developments:

• The Topology of Synergy (2025): Connecting topological approaches with information theory to quantify synergy and emergence in complex systems
• Uncertainty-Aware Methods: Frameworks that embed data quality and confidence directly into topological features rather than treating uncertainty as external noise
• Coherence in Social Systems: Sheaf-based models capturing hierarchical structure and information flow in complex social networks

Explore More: Full Publication List Software & Code Recent Talks