Simplicial Surfaces

 

In the winter term 2020/2021 Prof. Niemeyer will give a lecture about simplicial surfaces (see description below). The lecture can be attended by any student of a mathematics course (bachelor, master, teaching). To participate you only need some basic knowledge about groups, normally learned in a first algebra course (i.e. Computeralgebra).

In many areas of engineering objects may be assembled from smaller components. Practical considerations may constrain the shape of these components. In this course we are interested in surfaces constructed from triangles and in particular those controlled by a single congruence type of triangle.

Such simplicial surfaces can be described and investigated with combinatorial methods and their
combinatorial structure can be described using groups. We discuss several aspects of such surfaces, including their construction via geodesics and by other means, study properties of such surfaces and algorithms to work with them. It is a very hard problem to decide whether a surface has an embedding
into Euclidean 3-space, which we will briefly touch upon.

Investigations of simplicial surfaces controlled by a single triangle can be conducted with the help of the GAP-package "SimplicialSurfaces".

Registration takes place via RWTH online and learning material will be distributed in RWTHmoodle.