Prof.Martin Ziegler (KAIST)
-Titile: Theoretical Computer Science for Numerics
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
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.