Lattice points in convex sets - Geometry and optimization

Optimization is one of the mathematical fields that has developed rapidly in recent decades. On the one hand, this has to do with the diverse applications (e.g. in economics) and, on the other hand, certainly also with the improved possibilities of computer use.

Here we will focus on the sub-area of so-called "integer optimization", i.e. the search for "optimal" grid points in given convex areas of the plane, three-dimensional space or even higher-dimensional spaces.

In addition to motivating application examples, topics such as polyhedron theory, assignment problems, the traveling salesman problem, Minkowski's lattice point theory and linear form theorem as well as packing problems will be discussed.

Program

09.30 - 09.45Welcome Prof. Dr. W. Klotz
09.45 - 10.45Integer linear optimization: the difficulties of finding an optimal lattice point in polyhedra (Prof. Dr. P. Huhn)
10.45 - 11.15Coffee break
11.15 - 12.15Integer linear optimization: simple and difficult examples (Prof. Dr. P. Huhn)
12.15 - 13.30Lunch break
13.30 - 14.30Geometry of numbers: Minkowski's fundamental theorem with examples (Prof. Dr. J. Sander)
14.30 - 15.00Coffee break
15.00 - 16.00Lattice problems and applications (Prof. Dr. J. Sander)
16.00 - 16.30Discussion and closing remarks