Around quantitative Oppenheim conjecture We will explain properties of geometry and dynamics on homogeneous space that are used to prove a quantitative version of Oppenheim conjecture, which was proved by Eskin-Margulis-Mozes for the real case. We will introduce analogous statement in S-arithmetic case, which we proved in a joint work with K. Mallahi-Karai and J. Han. We will report preliminary observations for the case of signature (2,2).