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Applied topology: motivations from systems' euler characteristic intro motivations from networks, sensors, robotics, etc.
Computing homology 1: theory' intro to exact sequences
Consensus and distributed computation' not so sure about this one...
Homology 2' morse, morse-conley, hodge & more: simple applications
Mathematics Making Sense of Sensors
Network coverage via homology' coverage in sensor networks
Sensor networks and coverage
Sheaves and Euler integration' Euler integration and target enumeration
The Categorification of Applied Mathematics
Topological signal processing' target localization; integral transforms and euler calculus
Topology & systems: The future'
Unimodal decompositions' lyusternik-schnirelman category; unimodal category and mode-decomposition in statistics; applications to coordinate-free data