What are...alpha shapes and complexes?

Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.
This time.
What are...alpha shapes and complexes? Or: Topology and its applications.
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.
en.wikipedia.o...
demonstrations...
Main discussion.
Section II.5 of link.springer....
Chapter 3 of www.maths.ed.a...
courses.cs.duk...
graphics.stanf...
en.wikipedia.o...
en.wikipedia.o...
mathscinet.ams...
Background material.
bookstore.ams....
nmd.web.illinoi...
topology-tool-...
hcsoso.github....
arxiv.org/pdf/...
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
pi.math.cornel...
Mathematica.
demonstrations...
Pictures used.
Many pictures from link.springer....
Many more pictures from www.maths.ed.a...
Picture from • What is...homotopy?
employees.csbs...
RUclips and co.
• Voronoi diagram, Delau...
• What is...persistent h... (Shameful selfpromotion)
• An introduction to per...
• Applied topology 8: An...
• Persistent Homology wi...
#topology
#computerscience
#mathematics

[@jackhanson1274]

Thank you for the great lecture, I've just started using AlphaShapes for some research work I'm doing, great to have a concise breakdown of the basics! Thank you again!

[@VisualMath]

You are very welcome. I am glad that you liked the video and the story itself 😀

[@francoisgatine4106]

Amazing stuff ! Thank you for making so many videos on so many diverse topics !

[@VisualMath]

I am glad that you like my choice of topics.
My choices are certainly biased (sorry for that!). Here, for example, I am just a big fan of applied topology ;-) It is very strange: with many fields of math, topology included, one learns them in a vacuum and much later one realizes that they are super applicable - which is so fantastic! (This is also a hint that we might need to rethink how math is taught at uni right now - why do I need to wait years before I see applications? Not saying I have any idea how to change that...sorry...just ramble.)

[@1.4142]

I would study math if university classes were less dry and more focused on applications. Meanwhile, youtube videos like this are a great entry point.

[@VisualMath]

Thanks for the comment: I felt the same during my studies a trillion years ago (not much has changed...) but was too stupid to quit math ;-)
Focusing on the "pure part" is the classical approach to teach math. Its difficult to change that - or rather, changes are happening but very slowly. I am not saying one needs to agree that there is something to be changed: there is clearly some beauty in "abstract nonsense". I personally like both, abstract and applied, and I would like to see them going hand-in-hand. Not just in research where this is happening all the time, but also in teaching.

[@themathguy3149]

I just love some abstract nonsense! 😂

[@VisualMath]

Hah, I can feel you. But I like applied abstract nonsense even more ;-)