Zoom: register here: https://www.ntwebseminar.org/

## Number Theory Web Seminar: Samir Siksek (University of Warwick)

**The Fermat equation and the unit equation**

The asymptotic Fermat conjecture (AFC) states that for a number field K, and for sufficiently large primes p, the only solutions to the Fermat equation X^p+Y^p+Z^p=0 in K are the obvious ones. We sketch recent work that connects the Fermat equation to the far more elementary unit equation, and explain how this surprising connection can be exploited to prove AFC for several infinite families of number fields. This talk is based on joint work with Nuno Freitas, Alain Kraus and Haluk Sengun.

For further information about the seminar, please visit this webpage.

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