Thurston's quadratic Dehn function conjecture for $SL(n;\mathbb{Z})$

Let $n\geq 4$ and consider the arithmetic group $SL(n;\mathbb{Z})$, whose Dehn function measures the minimal filling area of null-homotopic loops in a finite presentation.

Thurston's conjecture. When $n\geq 4$, $SL(n;\mathbb{Z})$ has a quadratic Dehn function.

For these groups, the Dehn function is known to be bounded above by an exponential function, while the conjectured quadratic bound would substantially improve the general estimate. The claim is presented as an open conjecture in the source.