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.
www.dtubbenhauer.com/youtube.html
Website with exercises.
www.dtubbenhauer.com/lecture-a...
Thumbnail.
Picture from the first video slides.
Classical algebraic geometry.
en.wikipedia.org/wiki/Algebra...
en.wikipedia.org/wiki/Commuta...
en.wikipedia.org/wiki/Multiva...
en.wikipedia.org/wiki/Algebra...
en.wikipedia.org/wiki/Affine_...
en.wikipedia.org/wiki/Project...
en.wikipedia.org/wiki/Quasi-p...
en.wikipedia.org/wiki/Line_(g...)
en.wikipedia.org/wiki/Circle
en.wikipedia.org/wiki/Parabola
en.wikipedia.org/wiki/Ellipse
en.wikipedia.org/wiki/Hyperbola
en.wikipedia.org/wiki/Cubic_p...
en.wikipedia.org/wiki/Ellipti...
Modern algebraic geometry.
en.wikipedia.org/wiki/Algebra...
en.wikipedia.org/wiki/Scheme_...)
en.wikipedia.org/wiki/Formal_...
en.wikipedia.org/wiki/Ind-scheme
en.wikipedia.org/wiki/Algebra...
en.wikipedia.org/wiki/Algebra...
Modern algebraic geometry version 2.
en.wikipedia.org/wiki/Algebra...
en.wikipedia.org/wiki/Gr%C3%B...
en.wikipedia.org/wiki/Cylindr...
en.wikipedia.org/wiki/Tropica...
Applications of (algebraic) geometry.
math.stackexchange.com/questi...
Pictures used.
en.wikipedia.org/wiki/Maximum...
Pictures from www.dtubbenhauer.com/geotop20...
Picture from en.wikipedia.org/wiki/Complex...
Picture from • What is...the identity...
dictionary.cambridge.org/dict...
Some books I am using (I sometimes steal some pictures from there).
agag-gathmann.math.rptu.de/cl...
www.cambridge.org/core/books/...
bertini.nd.edu/book.html
mathoverflow.net/questions/24...
Computer talk.
magma.maths.usyd.edu.au/magma...
reference.wolfram.com/languag...
#algebraicgeometry
#geometry
#mathematics

[@mojedsamad7184]

thank you!

[@VisualMath]

Welcome 😀

[@jshores4318]

Oh yeah!! Your videos are excellent! I suggest them to all of my friends.

[@VisualMath]

Haha, thanks. I hope your friends are all into AG 🤣

[@pseudolullus]

12:03 I didn´t really get the term either, until I accidentally found out that it actually is "faisceau" in French. So a bundle basically, but the term is already in use for other mathematical objects.

[@VisualMath]

Ah, excellent. Thanks, that might be helpful. I personally prefer the name sheaf but that might be just that I got used to it 😅

[@pseudolullus]

@@VisualMath yes, it avoids confusion wrt well, bundles. But the mental image certainly helps

[@user-qp2ps1bk3b]

very nice video!

[@VisualMath]

Thanks, I am glad that you liked the video ☺

[@AnarchoAmericium]

Oh no! It was all a trick to teach us topos theory secretly!

[@VisualMath]

You did a great job figuring that out 🤣