Michele Caselli, a mathematician at Princeton University, presents a research seminar at the Institute for Advanced Study on nonlocal minimal surfaces. He opens with Yau's 1980s conjecture that every closed Riemannian 3-manifold contains infinitely many smooth minimal hypersurfaces, then builds toward a parallel existence result for the nonlocal, fractional version of minimal surfaces, showing how the classical Yau conjecture can be recovered as a special case. The core of the talk works through min-max methods applied to fractional perimeter functionals and a compactness and regularity theory for the resulting critical points, establishing full smoothness in low dimensions and a small singular set in higher ones. Time permitting, Caselli sketches a broader program extending these techniques to higher codimension surfaces. The talk is aimed at an audience already fluent in geometric analysis and minimal surface theory, delivered at the chalkboard pace typical of an IAS research seminar rather than a general survey.