S-Arithmetic Diophantine Approximation

In this Joint work with A. Salehi Golsefidy, we prove “S-arithmetic Khintchine
type theorems for non-degenerate manifolds”. In this talk I will define the
above mentioned terms and will draw the connection between Diophantine
approximation and flows on homogeneous spaces which goes back to S. G. Dani and
pushed much further by Kelinbock and Margulis. This result will serve as one
side of the dichotomy one would like to have for non-degenerate manifolds,
which was proved in the real case by Beresnevich, Bernik, Kleinbock and
Margulis.