What is...the Hodge conjecture?
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 intuitively? 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) • Video #algebra #geometry #mathematics

What is...P versus NP?

Where Did Algebra Really Come From?

Why colliding blocks compute pi

What is algebraic topology?

Poincaré Conjecture - Numberphile

Burt Totaro, The Hodge Conjecture: geometry and analysis
![Michael Atiyah: Poincaré conjecture, Hodge conjecture, Yang-Mills, Navier-Stokes [2000]](https://i.ytimg.com/vi/jQEdHOZscw4/hqdefault.jpg?sqp=-oaymwEjCNACELwBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLBbHzfvu6NY4vpZuvzDgMzolh5Y0Q)
Michael Atiyah: Poincaré conjecture, Hodge conjecture, Yang-Mills, Navier-Stokes [2000]

Einstein Said Ramanujan Was Receiving Math From Somewhere That Science Will Never Be Able To Explain

The most beautiful formula not enough people understand

The derivative isn't what you think it is.

Daniel Freed, Hodge conjecture

Terence Tao on Grigori Perelman solving Poincare Conjecture | Lex Fridman Podcast Clips

But what is a Laplace Transform?

Yang-Mills, Hodge, and Birch and Swinnerton-Dyer - Million Dollar Equations Part 2 with Tom Crawford

The Pattern Nobody Can Prove (But Everyone Believes)

Pierre Deligne | What is the Hodge conjecture?

The Integral Explained Better Than School Ever Did

Navier-Stokes Equations - Numberphile

Terence Tao: Nobody Understands Why AI Actually Works

