Jarod Alper: A tale of two polynomials

We will begin by studying the history and significance of the determinant versus permanent question:  for a given integer n, what is the smallest integer m such that the permanent of an arbitrary n x n matrix can be computed by the determinant of an m x m matrix, where each entry is an affine linear combination of the original entries?  We will provide a summary of the main results and techniques relating to this question.  The main goal is to prove that when n=3, the smallest integer is m=7.  This is joint work with Mauricio Velasco and Tristram Bogart.