Winning of inhomogeneous badly approximable vectors

Badly approximable vectors are one of the central topics in Diophantine approximation due to their connection with homogeneous dynamics and other problems in number theory. Though being null in Lebesgue measure, these vectors are known to have 'thick' structure, e.g. full Hausdorff dimension, or even stronger, the winning property that was first proven by Schmidt in the unweighted setup in the 1960s. Recently, Beresnevich-Nesharim-Yang proved the existence of such structure for badly approximable vectors on non-degenerate analytic curves and also ambient Euclidean spaces, in the weighted setup and in the sense of even stronger winning properties-"(hyperplane) absolute winning". Our talk will discuss how to push these results from homogeneous setup to inhomogeneous setup. This is a joint work with Shreyasi Datta.