What are...representable matroids 2?

Описание: Goal.
Explaining basic concepts in the intersection of graph theory and algebra in an intuitive way.

This time.
What are...representable matroids 2? Or: How to rule out matrices.

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Disclaimer.
Graph theory is one of the most applicable fields of mathematics, essentially by birth, but also a very wide area of beautiful results and active research. So to be precise, this video series is mostly about the interaction between graphs, matrices and polynomials and their various friends. That is, algebraic methods are applied to problems regarding graphs, and potentially also the other way around.

Slides.
http://www.dtubbenhauer.com/youtube.html

TeX files for the presentation.
https://github.com/dtubbenhauer/My-Te...

Website with exercises.
http://www.dtubbenhauer.com/lecture-a...

Thumbnail.
https://upload.wikimedia.org/wikipedi...

Algebraic graph theory.
https://en.wikipedia.org/wiki/Algebra...
https://en.wikipedia.org/wiki/Adjacen...
https://en.wikipedia.org/wiki/Laplaci...
https://en.wikipedia.org/wiki/Spectra...
https://en.wikipedia.org/wiki/Tutte_p...
https://en.wikipedia.org/wiki/Chromat...
https://en.wikipedia.org/wiki/Bollob%...
https://en.wikipedia.org/wiki/Graph_p...

Graph theory.
https://en.wikipedia.org/wiki/Graph_(...)
https://en.wikipedia.org/wiki/Graph_(...)
https://en.wikipedia.org/wiki/List_of...
https://en.wikipedia.org/wiki/Network...
https://en.wikipedia.org/wiki/Tree_(g...)
https://en.wikipedia.org/wiki/Graph_c...
https://en.wikipedia.org/wiki/List_of...

Applications of (algebraic) graph theory.
https://www.zib.de/groetschel/teachin...
https://link.springer.com/book/10.100...
https://link.springer.com/book/10.100...
https://people.unipmn.it/fragnelli/di...
https://koreascience.kr/article/JAKO2...
https://math.stackexchange.com/questi...
https://math.stackexchange.com/questi...
https://math.stackexchange.com/questi...
https://en.wikipedia.org/wiki/PageRank
https://en.wikipedia.org/wiki/List_of...
https://towardsdatascience.com/what-i...
https://www.xomnia.com/post/graph-the...

Pictures used.
https://en.wikipedia.org/wiki/V%C3%A1...
Picture from    • What is...the Kuratowski-Wagner theorem?  
Picture from https://www.fi.muni.cz/~hlineny/paper...
https://en.wikipedia.org/wiki/Graph_m...
https://upload.wikimedia.org/wikipedi...
Picture from https://arxiv.org/pdf/1203.0090.pdf
https://upload.wikimedia.org/wikipedi...

Some books I am using (I sometimes steal some pictures from there).
https://www.win.tue.nl/~aeb/2WF05/spe... also:
https://link.springer.com/book/10.100...
https://www.math.arizona.edu/~kglasne... also: https://link.springer.com/book/10.100...
https://link.springer.com/book/10.100...
https://link.springer.com/book/10.100...
https://www.zib.de/groetschel/teachin... also:
https://link.springer.com/book/978184...
https://www.cambridge.org/core/books/...
https://diestel-graph-theory.com/ also: https://link.springer.com/book/10.100...
https://assets.cambridge.org/97805217...

Mathematica.
https://reference.wolfram.com/languag...
https://reference.wolfram.com/languag...
https://demonstrations.wolfram.com/to...

SageMath.
https://doc.sagemath.org/html/en/refe...

#graphtheory
#algebra
#mathematics