Abstract: 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.