Marta Pieropan

m-full zeroes of diagonal forms

m-full zeroes of diagonal forms correspond to Campana points on diagonal hypersurfaces. Their asymptotic growth rate is predicted by conjectures of a geometric nature and has been studied by Browning, van Valckenborgh and Shute for linear forms using the circle method. I will explain how the results extend to diagonal forms of higher degree in a large number of variables. This is joint work with Balestrieri, Brandes, Kaesberg, Ortmann, and Winter. I will also explain how the results extend to systems of forms in independent sets of variables where the size of the variables is measured by functions that mix the variables. This is joint work with Schindler. I will also comment of work in progress on S-integer m-full solutions of diagonal forms.