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Research Frontiers in Computational Homology and Cohomology

Develops computational methods for calculating homology and cohomology groups of simplicial and cellular complexes from empirical data.

Persistent Homology in Dynamic Cellular Architectures
Cohomological Invariants of Tissue Microenvironments
Topological Data Analysis of Molecular Spatial Networks
Sheaf Cohomology in Multicellular Organization
Computational Topology of Organ-Scale Morphogenesis
Spectral Sequences in Spatial Omics Integration
Homological Algebra of Cell-Cell Communication Landscapes
Persistent Cycles in Disease Progression Topology
Intersection Cohomology of Spatially Resolved Tissues
Topological Defects in Three-Dimensional Tissue Architecture

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