What are...sheaves, take 1?

Goal. Explaining basic concepts in the intersection of geometry and algebra in an intuitive way. This time. What are...sheaves, take 1? Or: Complex analysis again. 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-algebrageometry-2024.html Thumbnail. Picture from the first video slides. Classical algebraic geometry. https://en.wikipedia.org/wiki/Algebraic_geometry https://en.wikipedia.org/wiki/Commutative_algebra https://en.wikipedia.org/wiki/Multivariate_polynomial https://en.wikipedia.org/wiki/Algebraic_variety https://en.wikipedia.org/wiki/Affine_variety https://en.wikipedia.org/wiki/Projective_variety https://en.wikipedia.org/wiki/Quasi-projective_variety https://en.wikipedia.org/wiki/Line_(geometry) 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_plane_curve https://en.wikipedia.org/wiki/Elliptic_curve Modern algebraic geometry. https://en.wikipedia.org/wiki/Algebraic_geometry#Abstract_modern_viewpoint https://en.wikipedia.org/wiki/Scheme_(mathematics) https://en.wikipedia.org/wiki/Formal_scheme https://en.wikipedia.org/wiki/Ind-scheme https://en.wikipedia.org/wiki/Algebraic_space https://en.wikipedia.org/wiki/Algebraic_stack Modern algebraic geometry version 2. https://en.wikipedia.org/wiki/Algebraic_geometry#Computational_algebraic_geometry https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis https://en.wikipedia.org/wiki/Cylindrical_algebraic_decomposition https://en.wikipedia.org/wiki/Tropical_geometry Applications of (algebraic) geometry. https://math.stackexchange.com/questions/575181/real-life-applications-of-algebraic-geometry Pictures used. https://en.wikipedia.org/wiki/Maximum_modulus_principle#/media/File:Maximum_modulus_principle.png Pictures from https://www.dtubbenhauer.com/geotop2023/topology-complete.pdf Picture from https://en.wikipedia.org/wiki/Complex_manifold Picture from https://www.youtube.com/watch?v=GKql0AZIePQ https://dictionary.cambridge.org/dictionary/english/sheaf Some books I am using (I sometimes steal some pictures from there). https://agag-gathmann.math.rptu.de/class/alggeom-2021/alggeom-2021.pdf https://www.cambridge.org/core/books/computational-algebraic-geometry/B6E21C8B64D5FF95A88805910B18A006 https://bertini.nd.edu/book.html https://mathoverflow.net/questions/2446/best-algebraic-geometry-textbook-other-than-hartshorne Computer talk. https://magma.maths.usyd.edu.au/magma/handbook/part/15 https://reference.wolfram.com/language/ref/ContourPlot.html #algebraicgeometry #geometry #mathematics