Effective version of Oppenheim conjecture in dimension 4

Let Q be a non-degenerate indefinite quadratic form with at least 3 variables. In the 1980s Margulis proved the longstanding Oppenheim Conjecture, stating that unless Q is proportional to an integral form, the set of values Q attaining at the integer points is dense in R. In Margulis' seminal work, he prove the Oppenheim conjecture by showing every SO(2, 1)-orbit in SL_3(R)/SL_3(Z) is either periodic or unbounded. In this talk, I'll present recent effective results in this direction emphasizing a polynomial rate by Lindenstrauss--Mohammadi--Wang--Yang in dimension 3 and my recent work in dimension 4.