Explores the role of higher-order topological properties in complex networks using topological data analysis for structural break and price anomaly detection.
Explores higher-order interactions in brain networks using simplicial complexes and information theory, analyzing data from fMRI, financial time-series, and infectious diseases.
Delves into Topological Data Analysis, emphasizing the mathematical foundations of neural networks and exploring the manifold hypothesis and persistent homology.
Introduces the construction of quasi-categories from Kan enriched categories through defining simplicially enriched categories and constructing the simplicial nerve functor.
Explores the influence of complexity on ergodic properties of symbolic systems, presenting the Curtis-Hedlund-Lyndon Theorem and constructions of minimal subshifts.
