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.
www.dtubbenhaue...
TeX files for the presentation.
github.com/dtu...
Thumbnail.
A soccer ball picture that can be found somewhere (I forgot, try to google it)
Main discussion.
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
Background material.
en.wikipedia.o...
donut.topology...
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...)
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...)
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
Computer talk.
en.wikipedia.o...
en.wikipedia.o...)
donut.topology...
en.wikipedia.o...
Pictures used.
Pictures from • What is...the 3d Poinc...
More pictures from • What is...the 3d Poinc...
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
KZbin and co.
• Computational topology...
• Introduction to applie...
• Introduction to Persis...
• Persistent Homology | ...
• An introduction to per...
• What is...the 3d Poinc... (Shameful selfpromotion)
#topology
#computerscience
#mathematics

[@YuXuanLow]

hey im a undergraduate mathematics student from Singapore and im really appreciative of these videos, thanks for making them!

[@VisualMath]

Thanks for the feedback and greetings back to Singapore (love that place 😀)

[@samhanna2349]

I like the volume level currently. Now keep it this way so each time I watch new video of yours, I don't have to adjust the volume :)

[@VisualMath]

Thanks for the feedback. I will see what I can do 😀

[@eternaldoorman5228]

3:08 The book _Proofs and Refutations_ by Imre Lakatos is actually a fairly historically accurate account of this, except the names of the people involved have been changed. Presumably to protect the innocent! But there are some notes relating the conjectures and definitions to various historical figures. However, it is rather a long time ago that I read it so I may be talking nonsense!

[@VisualMath]

Interesting, I didn’t knew that, I will have a look. Thanks for sharing 👍

[@peabrainiac6370]

Just a small nitpick: a problem being in NP and co-NP doesn't mean that it is necessarily hard, does it? Since those classes both contain P. If it was also NP-hard that would of course be a different story, but as far as I know it's still unknown whether it is.

[@VisualMath]

Right. I took the "NP and coNP" as an indication that something is hard, but yes, it could still be "easy" 😀