He works in the area of mathematical physics; in particular direct and inverse spectral theory with application to completely integrable partial differential equations (soliton equations).

The title of his thesis supervised by Fritz Gesztesy was Spectral Theory for Jacobi Operators (1995).

In 2006 he was awarded with the prestigious START-Preis by the Austrian Science Fund (FWF).

His most important contributions are to the fields of Sturm–Liouville theory, Jacobi operators and the Toda lattice.

He also works in biomathematics, in particular in the novel area of breath gas analysis, and has written a successful undergraduate textbook (Mathematics for Computer Science, in German) with his wife Susanne Teschl.