What is...computational topology?
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...computational topology? Or: Subfields of mathematics 6.
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.
A soccer ball picture that can be found somewhere (I forgot, try to google it)
Main discussion.
https://en.wikipedia.org/wiki/Computa...
https://en.wikipedia.org/wiki/Unknott...
https://en.wikipedia.org/wiki/SnapPea
https://en.wikipedia.org/wiki/Computa...
https://en.wikipedia.org/wiki/Computa...
Background material.
https://en.wikipedia.org/wiki/Topolog...
https://donut.topology.rocks/
https://en.wikipedia.org/wiki/Persist...
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://en.wikipedia.org/wiki/SnapPea
https://en.wikipedia.org/wiki/Regina_...)
https://donut.topology.rocks/
https://en.wikipedia.org/wiki/Topolog...
Pictures used.
Pictures from • What is...the 3d Poincaré conjecture?
More pictures from • What is...the 3d Poincaré conjecture?
https://en.wikipedia.org/wiki/Triangu...
https://en.wikipedia.org/wiki/Tetrahe...
https://en.wikipedia.org/wiki/NP_(com...
https://en.wikipedia.org/wiki/Unknott...
YouTube and co.
• Computational topology: from theory to pra...
• Introduction to applied and computational ...
• Introduction to Persistent Homology
• Persistent Homology | Introduction & Pytho...
• An introduction to persistent homology
• What is...the 3d Poincaré conjecture? (Shameful selfpromotion)
#topology
#computerscience
#mathematics