Ample divisors on moduli spaces of weighted pointed rational curves,   with applications to log MMP for $\bar{M}_{0,n}$
  We introduce a new technique for proving positivity of certain divisor classes on $\bar{M}_{0,n}$ and its weighted variants. Our methods give an unconditional description of the spaces of symmetric weighted pointed rational curves as log canonical models of $\bar{M}_{0,n}$. 
Maksym Fedorchuk, David Ishii Smyth