Ullrich, a member at the Institute of Analysis, was presented with his venia docendi/habilitation certification for his post-doc dissertation titled "Random vs. Optimal Data for High-Dimensional Approximation", examining the extent by which the intrinsic difficulty of various numerical problems is dependent on the dimension, meaning the parameter number, demonstrating that some problems in high dimensions are in practice unsolvable on account of the so-called "curse of dimension".

In addition, the extent to which "random data" (as is common in machine learning, for example) can keep pace using theoretically optimal constructions was also analyzed using classical problems. In doing so, fundamental relationships were revealed that have resulted in finding solutions to approximation theory problems, some of which are over 50 years old.

Those pursuing a habilitation/post-doc undergo an academic evaluation in regard to special qualifications that proves their ability to independently conduct academic/scientific research and teach the entire depth and breadth of their selected subject area [facultas docendi], This, in turn, is the prerequisite to grant authorization to teach that particular subject area.