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
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