New effective bounds on the dimension of a linear system in $\mathbb   P^2$
  The main goal of this paper is to present an algorithm bounding the dimension of a linear system of curves of given degree (or monomial basis) with multiple points in general position. As a result we prove the Hirschowitz--Harbourne Conjecture when the multiplicities of base points are bounded by 11. 
Marcin Dumnicki, Witold Jarnicki