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by matt-noonan 1355 days ago
Here are a few off the top of my head, as a mathematician-turned-programmer who never has been an algebraic geometer.

- Elliptic curve cryptography (https://en.wikipedia.org/wiki/Elliptic-curve_cryptography)

- Grobner bases, with many applications. Example domains: coding theory, robotics, signal processing... (https://math.stackexchange.com/questions/32421/applications-...)

- Physics [solitons] (https://kasmana.people.cofc.edu/SOLITONPICS/)

- Physics [string theory] (https://royalsociety.org/~/media/people/new-fellows-2014/Pre...)

- Automata theory, via "tropical" algebraic geometry (https://link.springer.com/article/10.1007/s00233-019-09999-8)

This is not even considering applications of AG to other areas of pure mathematics, which are extensive.