A. Sophie Aiken

Geometric Analysis is a branch of mathematics that utilizes tools and techniques from partial differential equations to study questions about the curvature of a space. In particular, I study the existence and uniqueness of metrics (similar to distance functions) within a conformal class which admit constant curvature.

One prominent question in geometric analysis is the existence and classification of conformal manifolds with constant curvature. In the last 40 years many people have intensely studied singular curvature problems in Riemannian manifolds, in particular the construction of constant curvature metrics on compact manifolds with singularities, i.e. punctures. In joint work with Caju, Ratzkin, and Silva Santos, we produce many new examples of complete, constant Q-curvature metrics on a finitely punctured sphere by gluing together known examples.