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