Johanna Michor

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

Research grants

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

• FWF Project P 31651, "Transition asymptotics of Soliton equations"
  Duration: 11/2018 - 11/2023
  Project Website
• FWF Elise Richter Grant V120, "Long time asymptotics of Soliton equations"
  Duration: 05/2011 - 11/2018
  Project Website
  
• FWF Erwin Schrödinger Fellowship J2655, "Scattering theory for CMV operators and applications to completely integrable systems"
  Duration: 03/2007 - 12/2008
  Project Website
  
• ÖAW DOC research grant 21388, "Asymptotic analysis of Jacobi operators and applications to completely integrable systems"
  Duration: 10/2003 - 10/2004
  Publications:
  1. I. Egorova, J. Michor, and G. Teschl, Scattering theory for Jacobi operators with quasi-periodic background, Comm. Math. Phys., 264-3, 811-842 (2006).
  2. J. Michor, Scattering theory for Jacobi operators and applications to completely integrable systems, Doctoral thesis, University of Vienna, 2005.