After introducing the moduli space of stable n-pointed curves of genus zero and describing its cohomology algebra, we present an approach towards koszulity of this algebra for the case n=6, first developed by Natalia Iyudu. It utilizes the concept of potential algebras, which are algebras with relations generated by the derivatives of a cyclic polynomial.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/4234
[3] http://www.mpim-bonn.mpg.de/node/8502