I will discuss the local minimality of certain configurations for a nonlocal isoperimetric problem used to model microphase separation in diblock copolymer melts. I will show that critical configurations with positive second variation are local minimizers of the nonlocal area functional and, in fact, satisfy a quantitative isoperimetric inequality with respect to sets that are close in $L^1$. As a byproduct of the quantitative estimate, one gets new results concerning periodic minimal surfaces and the global and local minimality of certain configurations.http://cvgmt.sns.it/seminar/409/
