Title: On the existence of isoperimetric sets on nonnegatively curved spaces Abstract: In this presentation, I will deal with the isoperimetric properties of spaces with nonnegative curvature, placing special emphasis on the existence of isoperimetric sets in the non-compact case. Isoperimetric sets of any volume do exist in compact Riemannian manifolds. Conversely, it is possible to construct simple examples […]

Title: Carleson ε^2 conjecture in higher dimensionsAbstract: I will talk about a joint work with Xavier Tolsa and Michele Villa on a higher dimensional analogue of the Carleson ε^2 conjecture. In this work, we characterise tangent points of certain domains in Euclidean space via a novel "spherical" square function which measures whether the common boundary of the […]

Title: Frobenius-type results on submanifolds and currentsAbstract: The question of producing a foliation of the n-dimensional Euclidean space with k-dimensional submanifolds which are tangent to a prescribed k-dimensional simple vectorfield is part of the celebrated Frobenius theorem: a decomposition in smooth submanifolds tangent to a given vectorfield is feasible (and then the vectorfield itself is […]