Overview
Dr. Jeffres' field of investigation is Riemannian and complex differential geometry. In particular, she is interested in special metrics on manifolds that are noncompact or which have singularities. Special metrics are those for which some curvature is constant. Since the curvature is an expression in the derivatives of the metric, setting this equal to a constant yields a partial differential equation. Therefore, solution of these problems frequently also involves some PDE techniques. Related to this, Dr. Jeffres is also interested in the heat operator.
Information
I work in the areas of, or intersection of, differential geometry, partial differential equations, and analysis. My interests include metrics satisfying special curvature conditions. When the object is non-compact or singular, techniques involve microlocal analysis and asymptotic methods.
These last several years, I have taught undergraduate courses in Calculus, Linear Algebra, and Number Theory, and graduate level courses in Complex Differential Geometry and in Partial Differential Equations.