Any Facts about Newton Polygons

AI Thread Summary
Newton Polygons are useful in analyzing the properties of polynomials, particularly in the context of p-adic analysis and differential equations. They help determine irreducibility and can provide insights into the roots of polynomials. A suggested resource for further exploration is a paper from the University of British Columbia, which may contain relevant applications and examples. Additionally, incorporating smaller facts about their use in different mathematical contexts can enhance the talk. Overall, Newton Polygons offer a rich area for discussion in polynomial theory.
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I'm giving a talk in a few days about Newton Polygons for polynomials and I was wondering if anyone knew of a few (short) interesting uses I could discuss or perhaps a text with a chapter on the subject. I have a cool result about irreducibility and of course the basics but it would be nice to have a few smaller facts that I can fill 10 or 20 minutes with.

I'm using them to look at polynomials in the p-adics but I understand that they have some uses in DE's as well although I don't know much about them.

Thanks,
Steven
 
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