Introduction to Diophantine equations
Channel: Richard E Borcherds
Date: 2020-09-15

This is an introductory talk on Diophantine equations given to the mathematics undergraduate student association of Berkeley (https://musa.berkeley.edu/)

We look at some examples of Diophantine equations, such at the Pythagoras equation, Fermat's equation, and a cubic surface. The main theme of the talk is that one can find solutions of these equations geometrically, by drawing the corresponding curve or surface and then drawing straight lines through known solutions.

Further reading: The book
"Undergraduate algebraic geometry" by Miles Reid gives more information about the cubic curves in the talk. There are also some more advanced youtube talks on similar topics at the playlist
https://www.youtube.com/playlist?list=PL8yHsr3EFj53j51FG6wCbQKjBgpjKa5PX