What is...tropical geometry?

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...tropical geometry? Or: Subfields of mathematics 11.

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.
https://en.wikipedia.org/wiki/Tropica...

Main discussion.
https://www.ams.org/notices/200704/wh...
https://en.wikipedia.org/wiki/Tropica...
https://en.wikipedia.org/wiki/Tropica...

Background material.
https://arxiv.org/abs/1502.05950
https://link.springer.com/book/10.100...
https://bookstore.ams.org/gsm-161
https://math.berkeley.edu/~bernd/trop...
https://sites.math.washington.edu/~mo...
https://en.wikipedia.org/wiki/Tropica...
https://nlab-pages.s3.us-east-2.amazo...
https://hal.archives-ouvertes.fr/hal-...

Computer talk.
https://doc.sagemath.org/html/en/refe...
https://wangweikun.com/math-software/...
https://community.wolfram.com/groups/...
https://demonstrations.wolfram.com/Tr...

Pictures used.
Pictures from    • What are...ideals of sets?  
Pictures from https://arxiv.org/abs/2408.00949
https://upload.wikimedia.org/wikipedi...
https://www.mis.mpg.de/fileadmin/_pro...
Picture from    • What is...a tropical curve?  
Another picture from    • What is...a tropical curve?  
And another picture from    • What is...a tropical curve?  

YouTube and co.
   • Tropical Geometry - Lecture 1 - Plane...  
   • An introduction to tropical geometry:...  
   • What is tropical geometry?  

#geometry
#algebraicgeometry
#mathematics