What is...computational topology?

Описание: 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