# Mathematics Colloquia and Seminars

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### Powers of Linear Forms

**Algebra & Discrete Mathematics**

Speaker: | Bernd Sturmfels, UC Berkeley, Mathematics |

Location: | 2112 MSB |

Start time: | Fri, Feb 20 2009, 2:10PM |

What is the dimension of the space of polynomials of a certain degree that are annihilated by certain powers of fixed vector fields? We obtain explicit formulas by computing sagbi bases of Cox-Nagata rings. They count the number of lattice points in certain polytopes derived from root systems. For del Pezzo surfaces, Cox-Nagata rings are presented by quadratic polynomials, and, for the blow-up of projective n-space at n+3 points, this involves a beautiful connection between the Verlinde formula and phylogenetic algebraic geometry. This is joint work with Zhiqiang Xu.

Paper: arXiv:0803.0892