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I am doing an undergraduate research project and the topic I have been assigned is cluster algebras (an introduction). I was reviewing some bibliography and videos on the internet and the truth is I don't know where to start.

I have taken the following courses: algebra (not Galois theory), analysis, topology. I have notions of quivers and their representations.

If you could give me an outline or guidelines to start reading it would be very helpful. As well as bibliography. Thanks!

Arctic Char
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Juan Daniel Valdivia Fuentes
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    I had not heard of cluster algebras. But, looking at the Wikipedia, it looks like this is a new field of study, with most of the work done by Fromin and Zelevinsky. Both of whom have web pages with the articles that they have written on the subject. I think that is your bibliograpy. – Doug M Nov 07 '20 at 02:09

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There is a book in progress available by Fomin, Zelevinsky, and Williams. You can find the first 6 chapters here, here, and here. This gives enough material for an introduction, I think.

You can also look at a particular motivating example: total positivity and it's tests. A good survey of very slick results can be found here. I strongly recommend trying a few of the examples, and thinking through these proofs. They helped me a lot.

Finally, there are a collection of lecture notes and old courses here. I have not reviewed them myself, so the quality of links and material may vary wildly.

Artimis Fowl
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