What is...additive combinatorics?
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...additive combinatorics? Or: Subfields of mathematics 2.
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.
Picture from https://en.wikipedia.org/wiki/Set_(ca...)
Main discussion.
https://en.wikipedia.org/wiki/Additiv...
https://www.cambridge.org/core/books/...
https://math.bme.hu/~gabor/oktatas/Sz...
https://yufeizhao.com/gtacbook/gtacbo...
https://en.wikipedia.org/wiki/Set_(ca...)
https://en.wikipedia.org/wiki/Cap_set
Background material.
https://en.wikipedia.org/wiki/Combina...
https://en.wikipedia.org/wiki/Graph_t...
https://en.wikipedia.org/wiki/Group_t...
https://en.wikipedia.org/wiki/Analysis
https://en.wikipedia.org/wiki/Ergodic...
https://en.wikipedia.org/wiki/Cyclic_...
https://en.wikipedia.org/wiki/Arithme...
https://en.wikipedia.org/wiki/General...
https://en.wikipedia.org/wiki/Restric...
https://en.wikipedia.org/wiki/Roth%27...
https://en.wikipedia.org/wiki/Restric...
https://en.wikipedia.org/wiki/Freiman...
Computer talk.
https://doc.sagemath.org/html/en/prep...
https://stackoverflow.com/questions/7...
Pictures used.
https://media.geeksforgeeks.org/wp-co...
https://coolmath.com/sites/default/fi...
Picture from https://en.wikipedia.org/wiki/Cyclic_...
https://en.wikipedia.org/wiki/Set_(ca...
https://media.cheggcdn.com/media/631/...
https://cdn.programiz.com/sites/tutor...
https://upload.wikimedia.org/wikipedi...
YouTube and co.
• Introduction to additive combinatorics lec...
• 1. A bridge between graph theory and addit...
#combinatorics
#numbertheory
#mathematics