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Discrete Mathematics

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Discrete Mathematics

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Research Frontiers in Topological Data Analysis and Persistent Homology

Investigation of persistent homological features in simplicial complexes derived from discrete data to understand topological structures at multiple scales.

Temporal Dynamics of Persistence Diagrams in Evolving Systems

Multiparameter Persistence and Algebraic Stability Landscapes

Topological Inference Beyond the Vietoris-Rips Complex

Persistent Homology in High-Dimensional Data Manifolds

Barcodes as Invariants for Machine Learning Classification

Computational Bottlenecks in Persistent Cohomology Algorithms

Functorial Properties of Persistence Across Filtrations

Noise Robustness and Stability of Topological Features

Persistent Homology for Time-Varying Graph Structures

Categorical Approaches to Multidimensional Persistence Modules

All Discrete Mathematics PhD categories