1,197 views since Nov 26, 2023

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 is...the Hodge conjecture? Or: Topology and algebraic geometry.

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/Orienta...
https://en.wikipedia.org/wiki/Kummer_...

Main discussion.
https://en.wikipedia.org/wiki/Hodge_c...
https://mathoverflow.net/questions/54...
https://burttotaro.wordpress.com/2012...
https://webusers.imj-prg.fr/~claire.v...
https://www.claymath.org/millennium/h...
https://www.redalyc.org/journal/5117/...
https://www.theguardian.com/science/b...
https://en.wikipedia.org/wiki/Millenn...

Background material.
https://en.wikipedia.org/wiki/Project...
https://en.wikipedia.org/wiki/Complex...
https://en.wikipedia.org/wiki/Homolog...)
https://en.wikipedia.org/wiki/Hodge_t...
https://en.wikipedia.org/wiki/Hodge_t...
https://en.wikipedia.org/wiki/Hodge_s...
https://en.wikipedia.org/wiki/De_Rham...
https://en.wikipedia.org/wiki/Weil_co...
https://en.wikipedia.org/wiki/Poincar...
https://en.wikipedia.org/wiki/Fundame...
https://en.wikipedia.org/wiki/Algebra...

Computer talk.
https://doc.sagemath.org/html/en/refe...
https://doc.sagemath.org/html/en/refe...

Pictures used.
https://en.wikipedia.org/wiki/Complex...
Picture from    • What is...the cohomology ring intuiti...  
https://en.wikipedia.org/wiki/Kummer_...
https://en.wikipedia.org/wiki/Complex...
https://www.researchgate.net/publicat...

YouTube and co.
claymath.msri.org/hodgeconjecture.mov
   • The Hodge Conjecture (Part 1)  
   • The Hodge Conjecture (Part 6---last)  
   • Geometers Abandoned 2,000 Year-Old Ma...  

#algebra
#geometry
#mathematics