Title: Chabauty for Symmetric Powers of Curves

Abstract: Let $C$ be a curve of genus $g\geq 3$ and
let $C^{(d)}$ denote its $d$-th symmetric power. We
explain an adaptation of Chabauty which allows us in
many cases to compute $C^{(d)}(\Q)$ provided the rank
of the Mordell-Weil group is at most $g-d$. We
illustrate this by giving two examples of genus $3$,
one hyperelliptic and the other plane quartic.