Geometry & Discrete Mathematics

Geometrie und diskrete Mathematik: Cyklide

Geometry and discrete mathematics: Classical model of a Dupin ring cyclide, annotated with characteristic ortho-circles


Geometry and discrete mathematics play an important role in applications, as well as in fundamental mathematics research. These both form the basis for theoretical understanding, the analysis of situations and the composition of orderings. 

As a classical discipline within mathematics, geometry questions the interaction between objects in a given space. Discrete mathematics structures the many variations, in which the objects stand in relation to one another.  


In our department, geometry covers the whole spectrum: from classical differential geometry and elementary geometry, to algebraic aspects of geometry and also combinatorial geometry, which studies the relative positions of objects. 

The sub-areas make it possible to view research themes as a whole, incorporating many different aspects: purely geometric, algebraic and analytic viewpoints, as well as discrete perspectives. Thereby, we focus equally upon fundamental aspects of geometric structures as upon specific applications which demand a deeper geometric understanding in order to analyze or visualize structures.  

Discrete mathematics

At the TUM Department of Mathematics, discrete mathematics are in close contact and exchange with the geometric and algebraic disciplines. We exploit the complete spectrum available: combinatorics, discrete geometry and polytope theory, as well as discrete differential geometry and optimization. Particularly in practice, analyses of discrete structures often play a significant role. 

The close connection of geometry and discrete mathematics to algorithmic questions, such as route planing and scheduling, chip layout, discrete tomography or data-analysis, visualizations and geometric kinematics round off the portfolio. 

Research areas

Our group for geometry and discrete mathematics at the TUM covers the fields of:

  • algebraic geometry
  • fundamentals of computer-aided geometry
  • discrete differential geometry
  • discrete optimization
  • combinatorial optimization
  • polytope theory
  • geometric invariant theory


Related research groups