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 Riemann-Roch theorem? Or: Allowing poles.
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-TeX-files
Thumbnail.
https://en.wikipedia.org/wiki/Holomorphic_function#/media/File:Gamma_abs_3D.png
Main discussion.
https://en.wikipedia.org/wiki/Riemann%E2%80%93Roch_theorem
https://web.ma.utexas.edu/users/gregoric/Baby%27s%20Riemann-Roch.pdf
https://en.wikipedia.org/wiki/Holomorphic_function
https://en.wikipedia.org/wiki/Meromorphic_function
https://en.wikipedia.org/wiki/Maximum_modulus_principle
Background material.
https://en.wikipedia.org/wiki/Complex_analysis
https://en.wikipedia.org/wiki/Algebraic_geometry
https://en.wikipedia.org/wiki/Differentiable_function#Differentiability_in_complex_analysis
https://en.wikipedia.org/wiki/Polynomial
https://en.wikipedia.org/wiki/Rational_function
https://en.wikipedia.org/wiki/Power_series
https://en.wikipedia.org/wiki/Smoothness
https://en.wikipedia.org/wiki/Taylor_series
https://en.wikipedia.org/wiki/Riemann_surface
https://en.wikipedia.org/wiki/Genus_(mathematics)
Computer talk.
https://reference.wolfram.com/language/ref/FunctionAnalytic.html
https://reference.wolfram.com/language/ref/FunctionMeromorphic.html
https://reference.wolfram.com/language/ref/FunctionSingularities.html
Pictures used.
https://en.wikipedia.org/wiki/File:Conformal_map.svg
https://en.wikipedia.org/wiki/Holomorphic_function#/media/File:Gamma_abs_3D.png
https://en.wikipedia.org/wiki/Maximum_modulus_principle#/media/File:Maximum_modulus_principle.png
https://en.wikipedia.org/wiki/Zeros_and_poles#/media/File:Pole-order9-infin.png
Again https://en.wikipedia.org/wiki/Zeros_and_poles#/media/File:Pole-order9-infin.png
https://en.wikipedia.org/wiki/Riemann%E2%80%93Roch_theorem#/media/File:Triple_torus_illustration.png
YouTube and co.
https://www.youtube.com/watch?v=uRfbnJ2a-Bs
https://www.youtube.com/watch?v=1IZcnuQ7T8k
https://www.youtube.com/watch?v=bCSF-B3EhO0
#geometry
#analysis
#mathematics