My research lies generally in the area of geometric analysis where I use analysis of PDEs to study geometric properties of conformal manifolds. More specifically I work on Yamabe-type problems searching for conformal metrics that admit constant curvature, including higher order, singular, and fractional order problems.
For an introduction to the Yamabe Problem, I recommend the 1987 survey The Yamabe Problem by Lee and Parker.
Preprints
A. Sophie Aiken, Rayssa Caju, Jesse Ratzkin, and Almir Silva Santos. An end to end gluing construction for metrics of constant Q-curvature. 2025. arXiv: 2503.09234 [math.DG]. URL: https://arxiv.org/abs/2503.09234.
In Preparation
A. Sophie Aiken. A note on the classical and fractional Yamabe problem.Â