Let $(p,q)$ be a pair of coprime (positive) integers. Consider the torus knot $T_{p,q}$. What is the minimal genus of an (embedded) oriented Seifert surface for this knot?

It is not had to convince oneself that in the simplest case $p =2$, there is a Seifert surface of genus $(q-1)/2$. I do not know whether that is optimal.