# Mathematics Colloquia and Seminars

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### Hyperdeterminants of polynomials

**Algebra & Discrete Mathematics**

Speaker: | Luke Oeding, UC Berkeley |

Location: | 2112 MSB |

Start time: | Tue, Apr 10 2012, 2:10PM |

Hyperdeterminants were brought into a modern light by Gelʹfand, Kapranov, and Zelevinsky in the 1990's. Inspired by their work, I will answer the question of what happens when you apply a hyperdeterminant to a polynomial (interpreted as a symmetric tensor). The hyperdeterminant of a polynomial factors into several irreducible factors with multiplicities. I identify these factors along with their degrees and their multiplicities, which both have a nice combinatorial interpretation. The analogous decomposition for the μ-discriminant of polynomial is also found. The methods I use to solve this algebraic problem come from geometry of dual varieties, Segre-Veronese varieties, and Chow varieties; as well as representation theory of products of the general linear group.