Barcode Admissible Persistence Modules

My research applies algebraic topology and differential geometry to data analysis, concentrating on Morse theory and its relevance to multiparameter persistence homology. I investigate multiparameter persistence modules' invariants and barcode admissibility (i.e., decomposability into simpler modules) to understand the topological features these barcodes represent. The goal is to deepen our comprehension of data shapes, exploring dimensions that statistical methods might miss. 

TDA ongoing Projects (Dec 2024):

• Developing efficient algorithms for detecting barcode-admissible persistence modules (Github Page).

• Exploring relationships between discrete invariants and multiparameter barcodes, emphasizing computational aspects. 

• Providing geometric interpretations of barcode admissibility in the context of Multiparameter Morse theory

ML-TDA ongoing Projects (Aug 2024):

• Enhancing machine learning models by providing additional input features from multiparameter TDA techniques. 

• Vectorization of multiparameter modules and their barcodes (if available).