# Research Unit *Applied Geometry and Discrete Mathematics* (M9)

Welcome the the research unit *Applied Geometry and Discrete Mathematics*. Our work is focussed on geometric representations of optimization problems and their solution. Using descriptions of feasible solutions as points in a very large, high-dimensional search space, combinatorial constraints can be translated into geometric characteristics. A better understanding of these characteristics, as is often possible by looking at the problems from a combined geometric, combinatorial and discrete mathematics viewpoint (e.g., using results from graph theory, matroid theory, polyhedral geometry and combinatorics) enables us to devise powerful algorithmic approaches to solve very complex optimization problems. Such problems occur in a variety of applied projects, for example in routing, logistics, scheduling, microchip layout, discrete tomography or data analysis. If you want to know more about applications of our work, have look at the projects page.