The restricted invertibility principle asserts that every square matrix L with unit length columns contains a large column submatrix whose least singular value is bounded away from zero. We will give a short, elementary proof of a sharp version of this principle based on the method of interlacing polynomials. The proof avoids technical calculations, and relies on classical estimates for the roots of Laguerre polynomials. Speaker(s): Alon Nishry (University of Michigan)