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Classroom Contents
Geometry and Topology of Periodic Point Sets, for Example Crystals
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- 1 Intro
- 2 Overview
- 3 What is a (periodic) crystal?
- 4 What is a periodic crystal not?
- 5 Periodic point set
- 6 Finite representation not unique
- 7 Define equivalence relation
- 8 Computing distance
- 9 Comparing crystals
- 10 Why do we want a fingerprint function?
- 11 Packing and covering radii
- 12 Proof Sketch: Computability using Brillouin zones
- 13 The density fingerprint and the persistence fingerprint!
- 14 Persistent homology
- 15 Order k persistence
- 16 Definition (Persistence fingerprint function )
- 17 Definition: Infinitely many holes
- 18 Definition: Torus
- 19 Definition: Features per volume
- 20 Computing: Features per volume
- 21 Definition (Persistence fingerprint function 4)
- 22 Capturing non-cubic cycles
- 23 Future Work
- 24 Bibliography
- 25 Alternative distance between crystals
