Research Interests

Harmonic Analysis, Partial Differential Equations, and Geometric Analysis.
In particular, I am interested in doing analysis in “rough” settings and determining how the geometric make-up of the underlying environment can influence the type of analysis which can be performed.

Some topics include:

  • analysis in spaces of homogeneous type
  • smoothness spaces (Hardy, Sobolev, Besov, Triebel-Lizorkin, Mixed-Norm,...)
  • second and higher order elliptic differential systems in various domains
  • boundary value problems
  • boundary integral methods
  • geometry of rough domains