What is...topological data analysis?
Goal.
I would like to tell you a bit about my favorite subfields of mathematics (in no particular order), highlighting key theorems, ideas or concepts and why I like them so much. This is a variation of “My favorite theorems” and I park the videos on that list as well.
This time.
What is...topological data analysis? Or: Subfields of mathematics 3.
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Slides.
http://www.dtubbenhauer.com/youtube.html
TeX files for the presentation.
https://github.com/dtubbenhauer/My-Te...
Thumbnail.
Picture from • What are...ringed spaces?
Main discussion.
https://en.wikipedia.org/wiki/Topolog...
https://donut.topology.rocks/
https://en.wikipedia.org/wiki/Persist...
Background material.
https://en.wikipedia.org/wiki/Computa...
https://en.wikipedia.org/wiki/Algebra...
https://en.wikipedia.org/wiki/Shape_a...)
https://en.wikipedia.org/wiki/Data_mi...
https://en.wikipedia.org/wiki/Persist...
https://en.wikipedia.org/wiki/Homolog...)
https://en.wikipedia.org/wiki/Topolog...
https://en.wikipedia.org/wiki/Simplic...
https://en.wikipedia.org/wiki/Vietori...
Computer talk.
https://donut.topology.rocks/
https://en.wikipedia.org/wiki/Topolog...
Pictures used.
Pictures from • What are...ringed spaces?
Pictures from • What are...alpha shapes and complexes?
Pictures from • What is...persistent homology?
https://datawarrior.wordpress.com/wp-...
Pictures from • What is...persistent homology?
YouTube and co.
• Introduction to Persistent Homology
• Persistent Homology | Introduction & Pytho...
• An introduction to persistent homology
• What is...persistent homology? (Shameful selfpromotion)
#topology
#dataanalysis
#mathematics