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Room P4.35, Mathematics Building
Nuno Freitas, Univ. Barcelona
Fermat-type equations of signature \((13,13,p)\) via Hilbert cuspforms
In this talk I will give an introduction to the modular approach to
Fermat-type equations via Hilbert cuspforms and discuss how it can
be used to show that certain equations of the form have no solutions such that and if . We will first relate a putative
solution of the previous equation to the solution of another
Diophantine equation with coefficients in . Then we
attach Frey curves over to solutions of the
latter equation. Finally, we will discuss on the modularity of
and irreducibility of certain Galois representations attached to
it. These ingredients enable us to apply a modular approach via
Hilbert newforms to get the desired arithmetic result on the
equation.
Duration 90 minutes or slightly less