The goal of this REU is use tools from linear algebra (in particular, lattices) to obstruct knots and links from bounding Euler characteristic 1 surfaces in the 4-ball (such links are called chi-slice). At the beginning of the summer, we will explore why such knots and links are interesting, how they can be used to construct particular 3-dimensional and 4-dimensional manifolds, and how linear algebra has anything to do with such geometric ideas. We will then begin working on classifying which links are chi-slice for particular families of links.