Mathematical Fields
For the planned research work in the Center, the following
three mathematical fields have turned out to be crucial. They
are well represented in Berlin and have been selected as the
main fields contributing to the Center.
|
| |
|
I: Optimization and discrete mathematics
|
Scientists in Charge:
Werner Römisch,
Martin Skutella,
Günter M. Ziegler
|
Optimization is the task to maximize or minimize an objective function under side constraints.
Discrete mathematics is the area where integrality issues (integral variables or yes/no decisions) dominate the mathematical structure.
The two fields overlap in integer programming, for instance, where a linear objective function has to be optimized over the set of integral points in a polyhedron. These fields started to grow together - driven by applications that require the joint investigation of integrality, nonlinearity, and even stochastic aspects.
|
|
| |
|
II: Numerical analysis and scientific computing
|
Scientists in Charge:
Ralf Kornhuber,
Reinhold Schneider,
Harry Yserentant
|
The scientific discipline numerical analysis deals with the construction and analysis of efficient numerical algorithms for the solution of mathematical problems.
Already since the 1950's, this discipline has played an important role in the simulation and optimization of problems that arose from a variety of application areas, mostly from science, engineering, and economics.
In the course of time, numerical analysis has proved more and more successful in core engineering problems - as an example, take numerical wind tunnels that nowadays partly substitute actual wind tunnels.
As a result of this success, further areas from the applied sciences came into sight: More and more detailed mathematical models in new branches of technology like information and communication technology, medical technology, or biotechnology were designed; at the same time, for reasons of sheer computational complexity, numerical analysts were drawn into mathematical and scientific modelling as well.
|
|
| |
|
III: Applied and stochastic analysis
|
Scientists in Charge:
Peter Imkeller,
Alexander Mielke
|
|
The fields of applied analysis and of stochastic analysis play a fundamental role in the mathematical modelling of almost all non-discrete processes in nature, science, and economy. The fact that differential equations form a common language for such processes has been the basis of spectacular breakthroughs in the understanding of the physical world and in the development of engineering solutions over the last centuries. This impact of analysis has increased dramatically in the past decades, since the development of modern computer technology made the quantitative simulation of ever more complex systems of differential equations possible. In particular, the recent and future development of modern key technologies strongly depends on advances in applied and stochastic analysis. These fields will be of fundamental importance within the Center. This applies especially to all projects where differential equations occur in the models.
|
|
|
