What is...Hilbert’s Nullstellensatz?

Goal.
Explaining basic concepts in the intersection of geometry and algebra in an intuitive way.
This time.
What is...Hilbert’s Nullstellensatz? Or: The zero-locus-theorem.
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.
Pictures created using reference.wolfram.com/languag...
More pictures created using reference.wolfram.com/languag...
Even more pictures created using reference.wolfram.com/languag...
images.collegedunia.com/publi...
Pictures created using reference.wolfram.com/languag...
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

[@faustustuus3747]

In Polish we also call it "Nullstellensatz" (which sounds very elegant to my taste). Thanks for bringing this great series to YT, really looking forward to the future instalments!

[@VisualMath]

Excellent, thanks ☺

[@JAYMOAP]

Another great video

[@VisualMath]

Thanks, I am glad that you liked the video ☺

[@Rozenkrantzz]

Great vid, ty! Just one comment, the sound is really low, I struggle to hear. Otherwise, fantastic

[@VisualMath]

Thanks for the feedback. I have the impression that the sound is too loud, but let me see what I can do.