Abstract: The talk will take place in two parts. The first part is really about linear systems on projective space, but I will approach the problem from its application to interpolating data with polynomials in several variables. My goal is to make this part of the talk accessible at an undergraduate level. The second part deals with the minimal graded free resolutions of Veronese modules; ones which arise from a natural construction in algebraic geometry. I will give a proof of a certain duality theorem which requires only simplicial topology.