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Applied Mathematics

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Applied Mathematics

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Research Frontiers in Topological Data Analysis Methods

Application of algebraic topology techniques to extract persistent features and geometric structure from high-dimensional datasets.

Persistent Homology in Non-Euclidean Data Spaces
Topological Signatures of High-Dimensional Phase Transitions
Temporal Topology: Tracking Shape Across Dynamic Systems
Quantum Entanglement Detection via Persistent Diagrams
Topological Clustering in Noisy, Incomplete Datasets
Mapper Graphs for Discovering Hidden Data Stratification
Categorical Topology and Machine Learning Robustness
Barcodes and Bifurcations: Topology Meets Dynamical Systems
Topological Complexity of Neural Network Decision Boundaries
Sheaf-Theoretic Methods in Multi-Scale Data Analysis

All Applied Mathematics PhD categories