The Generalised Baker--Schmidt Problem (1970)
The Generalised Baker--Schmidt Problem, inspired by the pioneering work of Alan Baker and Wolfgang Schmidt (1970), is a central problem in metric Diophantine approximation on manifolds. It concerns the estimation of \(f\)-dimensional Hausdorff measure of the set of \(\psi\)-approximable points on a nondegenerate manifold. In this talk, I will explain resolution of this problem for a parabola, planar curves and hypersurfaces. These result are the first of their kind.
Mumtaz Hussain, La Trobe University