Erin Pearse
My research revolves around the study of complex dimensions. This is an extension of real-valued dimensions like Hausdorff or Minkowski/box dimensions. Richly structured sets (like fractals) typically have an infinite sequence of complex dimensions, and these may allow one to study connections between the geometry and spectrum of the set. I am especially interested in how the complex dimensions describe the "geometric oscillations" (that is, the oscillatory behavior of the tube
formula) of a set, and how this can be used to study the curvature of fractal sets. This theory touches on harmonic analysis, dynamical systems, geometric measure theory, and convex geometry. There are also many interesting applications to number theory, but this is not really my area of study.
In my spare time, I enjoy recreational cooking (and eating!), reading aloud, and going places with my wife and adorable baby daughter.