Brett Kotschwar's research is in the area of geometric analysis, at the intersection of the fields of differential geometry and partial differential equations. Differential geometry is the study of the properties of certain abstract curved spaces which generalize the familiar concepts of curves and surfaces in three-dimensional space. His research belongs to a broader program which explores the geometric and topological properties of these spaces -- roughly, how they bend and are put together -- through the study of the solutions they admit to various natural partial differential equations.
