Juan Morales
PIF Fellow
About
Juan Morales is a first year Ph.D. student in pure mathematics in the department of Mathematics, Statistics, and Computer Science. His main research interest centers in Riemannian geometry, complex and differentiable geometry in low-dimensional manifolds. One of the most fundamental question mathematics, and geometry in particular, attempts to answer is the search for an optimal representative within a certain class of objects. For example, given a closed curve in Euclidean space, we want to find a surface such that the curve is it’s boundary and has minimal area. Such surfaces are called minimal surfaces. We can interpret these in the following manner; minimal surfaces are the thin membrane a soap film would assume if one were to dip a wire frame, in the shape of our closed curve, into a soap solution and then lifted out. The theory of minimal surfaces has applications in theoretical physics, particularly in general relativity, molecular engineering, among other fields.