Editing Diophantine approximation (section)

== Recent developments ==
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In his plenary address at the [[International Mathematical Congress]] in Kyoto (1990), [[Grigory Margulis]] outlined a broad program rooted in [[ergodic theory]] that allows one to prove number-theoretic results using the dynamical and ergodic properties of actions of subgroups of [[semisimple Lie group]]s. The work of D. Kleinbock, G. Margulis and their collaborators demonstrated the power of this novel approach to classical problems in Diophantine approximation. Among its notable successes are the proof of the decades-old [[Oppenheim conjecture]] by Margulis, with later extensions by Dani and Margulis and Eskin–Margulis–Mozes, and the proof of Baker and Sprindzhuk conjectures in the Diophantine approximations on manifolds by Kleinbock and Margulis. Various generalizations of the above results of [[Aleksandr Khinchin]] in metric Diophantine approximation have also been obtained within this framework.