MSc (Mathematics+Physics) 1997 Paderborn University,
PhD (Computer Science) 2002 Paderborn University,
Habilitation/Venia Legendi (Computer Science) 2008 Paderborn University,
DFG Heisenberg Scholar 2009 Vienna University of Technology,
Associate Professor of Logic 2010-2015 Darmstadt Technical University
-Abstract
Theoretical Computer Science provides the sound foundation
and concepts underlying contemporary algorithm design and
reliable software development for discrete problems:
Problems in the continuous realm commonly considered in Numerical
Engineering are largely treated by 'recipes' and 'methods' whose
correctness and efficiency often rely on thin empirical evidence.
We extend and apply the rigorous theory of computation
(specification,
semantics, algorithm design, analysis, and proof of optimality) over
discrete structures to continuous domains. For instance it turns out that
famous complexity classes like P, NP, #P, and PSPACE naturally re-emerge
in the setting of real numbers, sequences, continuous functions,
operators, and Euclidean subsets including a reformulation of the
Millennium Prize Problem as a numerical one. Our current work develops a
computability and complexity classification for ordinary and partial
differential equations, the latter having weak solutions naturally
'living' in Sobolev space.