**abstract:**
Let S be a finite set of prime numbers.
We use Minhyong Kim's higher Chabauty method and the theory of mixed Tate motives to study the S-unit equation u + v = 1,
where u,v are S-units, i.e. units of the ring ZS^{-1}. Our ultimate goal is to construct a practical algorithm for finding all solutions to the S-unit equation whose halting is conditional on certain plausible conjectures on motivic and p-adic iterated integrals.

Fri 20 Dec, 9:15 - 10:15, Aula Dini

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