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What is...Schubert calculus?

Goal. Explaining basic concepts in the intersection of geometry and algebra in an intuitive way. This time. What is...Schubert calculus? Or: Intersecting spaces. Disclaimer. Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references. Disclaimer. In this course I try to cover my favorite topics in algebraic geometry, from classical ideas such as algebraic varieties, to modern ideas such as schemes, to really modern ideas such as tropical varieties. I give a very biased collection of topics, and not nearly all that can be said will be addressed. Sorry for that. Slides. http://www.dtubbenhauer.com/youtube.html Website with exercises. http://www.dtubbenhauer.com/lecture-a... Thumbnail. Picture from the first video slides. Classical algebraic geometry. https://en.wikipedia.org/wiki/Algebra... https://en.wikipedia.org/wiki/Commuta... https://en.wikipedia.org/wiki/Multiva... https://en.wikipedia.org/wiki/Algebra... https://en.wikipedia.org/wiki/Affine_... https://en.wikipedia.org/wiki/Project... https://en.wikipedia.org/wiki/Quasi-p... https://en.wikipedia.org/wiki/Line_(g...) https://en.wikipedia.org/wiki/Circle https://en.wikipedia.org/wiki/Parabola https://en.wikipedia.org/wiki/Ellipse https://en.wikipedia.org/wiki/Hyperbola https://en.wikipedia.org/wiki/Cubic_p... https://en.wikipedia.org/wiki/Ellipti... Modern algebraic geometry. https://en.wikipedia.org/wiki/Algebra... https://en.wikipedia.org/wiki/Scheme_...) https://en.wikipedia.org/wiki/Formal_... https://en.wikipedia.org/wiki/Ind-scheme https://en.wikipedia.org/wiki/Algebra... https://en.wikipedia.org/wiki/Algebra... Modern algebraic geometry version 2. https://en.wikipedia.org/wiki/Algebra... https://en.wikipedia.org/wiki/Gr%C3%B... https://en.wikipedia.org/wiki/Cylindr... https://en.wikipedia.org/wiki/Tropica... Applications of (algebraic) geometry. https://math.stackexchange.com/questi... Pictures used. https://stellabooks.com/storage/image... Picture from https://en.wikipedia.org/wiki/Hilbert... Pictures created using https://www.geogebra.org/calculator Picture from    • What is...the cohomology ring intuiti...   Again pictures created using https://www.geogebra.org/calculator Some books I am using (I sometimes steal some pictures from there). https://agag-gathmann.math.rptu.de/cl... https://www.cambridge.org/core/books/... https://bertini.nd.edu/book.html https://mathoverflow.net/questions/24... Computer talk. https://magma.maths.usyd.edu.au/magma... https://reference.wolfram.com/languag... #algebraicgeometry #geometry #mathematics