In 1985, Dani studied the connection between homogeneous dynamics and Diophantine approximation, which is called Dani's correspondence.
Since the breakthrough of the Sprindzuk conjecture by Kleinbock and Margulis, the dynamical method under Dani's correspondence has been widely used in the study of metric Diophantine approximation.
In this thesis, we mainly focus on the following three Diophantine objects: Dirichlet improvable affine forms; Badly approximable affine forms; Weighted singular vectors.
We review some recurrence properties of one-parameter flow and corresponding Diophantine properties.
Through this connection, we will discuss how dynamical methods give metrical results for the above three objects.
zoom link : https://snu-ac-kr.zoom.us/j/6617727733
ID : 661 772 7733