Title: Blow-Ups of Projective Space and Toric Vector Bundles

Abstract: Toric vector bundles are a rich class of varieties that relate to interesting topics in combinatorics, like matroids. In a paper published in 2012, Gonzalez, Hering, Payne, and Suss prove a nice geometric relationship with blow-ups of projective space that holds for certain toric vector bundles. We will introduce these objects and describe an approach to generalize this relationship to all toric vector bundles.