Prior to 1987:
  • mathematical theory of waves
  • magnetohydrodynamic waves
  • stability in astrophysics
  • applied spectral theory of singular ordinary differential equations arising in mathematical physics.

Since 1987:
  • mathematical biology
  • mathematical modeling, especially in the context of cancer biology
  • wound healing in bone

Since 2000:
  • mathematical theory of meteorological optics, both pedagogically and in terms of asymptotics and special functions