Continuity of critical points of Riesz energies in dimension 1

We will present a regularity result for critical points of Riesz energies in dimension 1 for a general class of interaction kernels assuming that the critical points admit bounded density with respect tothe Lebesgue measure. Under some convexity assumptions on the kernel, we provide a control on the oscillations of the density, yielding to the continuity result. The seminar is based on a work with N. Fusco and A. Pratelli