# Topological Data Analysis

I’m watching these lectures

https://www.youtube.com/watch?v=G3rWz2LgzZY

I am skeptical that this is useful, but it does seem interesting. Also, since their intent is for practical use, it won’t be so high falutin’

Lec 1. Sensor fusion and cross correlating sensors seems to be the idea. Tracking multiple objects. CoSheafs are something? More meat to come

Lec2. edges and faces are sources to be checked for consistency

Flag complexes or clique complex - every set of edges that could have a face has a face

star - all the higher dimensional simplices that contain that object

alexandrov topology - open sets are unions of stars

Nerve - open cover of X. for every set U in cover is vertex. for every intersection that is nonempy, there is a simplex. Leray Theorem

Lec3. Sheaves. you can associate a diagram of inclusion with your simplices. if every simplex has some space associated with it, then you can put functions on these inclusions. Then