harbater AT math.upenn.edu
My research involves the study of algebraic objects using ideas motivated by geometry with connections to number theory. Much of my work has focused on Galois theory and its generalizations. This includes the study of fundamental groups and covering spaces in algebraic geometry, e.g. covers of p-adic curves, as well as differential Galois theory. I also study local-global principles for arithmetic curves and their applications to the behavior of algebraic structures such as torsors, quadratic forms, and central simple algebras.