## Seminar:

Fall 2008, Thursdays, Milner 216, 4:00-4:50 PM
__ Date:__ ** October 9 **

**" The set theoretic defining equations of the variety of principal minors of symmetric matrices "**

**Luke Oeding**

__Abstract__A principal minor is the determinant of a submatrix centered about the main diagonal. An n by n matrix has 2^n principal minors. The map which takes a symmetric matrix to a vector of its principal minors defines the variety of principal minors of symmetric matrices. The equations of this variety tell when it is possible for a given vector of length 2^n to be the principal minors of a symmetric matrix. Holtz and Sturmfels conjectured that these equations would be given by the hyperdeterminantal module. In this talk, I will introduce the necessary representation theory to describe this module and I will sketch a proof of the set theoretic version of the Holtz and Sturmfels conjecture. My goal is to include enough examples so that everyone will get something out of this talk.