For a given null-homologous loop $\gamma$ in a space $X$, we minimize
complexities of surfaces bounding $\gamma$, where the complexity is
measured essentially by the Euler characteristic. The infimal complexity
is called the stable commutator length (scl) of $\gamma$ in $\pi_1(X)$.
Scl is a monotone group invariant and a relative version of the Gromov
norm. Surfaces realizing the minimal complexity are called extremal. When
exist, they are $\pi_1$-injective and can be used to find surface
subgroups.

In this talk, we explore scl in Baumslag--Solitar groups, including its
computation by linear programming, a criterion for the existence of
extremal surfaces, and a convergence to scl in free groups resembling
hyperbolic Dehn surgeries.