Johanna Michor

Department of Mathematics

Research interests

I am interested in completely integrable wave equations, or soliton equations, and applications of algebraic geometry and functional analysis to such systems.

Applied functional analysis

  • Inverse spectral theory (Jacobi matrices)
  • Trace formulas
  • Direct and inverse scattering theory (Jacobi operators)

Applied algebraic geometry

  • Algebro-geometric solutions
  • Hierarchies of completely integrable wave equations

Completely integrable systems

  • Inverse scattering transform
  • Riemann-Hilbert problems
  • Long-time asymptotics (nonlinear steepest descent method)
  • Stability of soliton equations (Toda, Ablowitz-Ladik)
The Toda shock wave with different regions of asymptotic behavior Image Image

Research grants

My research is supported by the following grants (PI Johanna Michor).