#
Monday Lecture and Colloquium

**Monday, June 23, 2014**

Freie Universität Berlin

Institut für Informatik

Takustr. 9

14195 Berlin

room 005

** Lecture - 14:15**

### Ulrich Brehm -
Technische Universität Dresden

### Universality Theorems in Geometry

*Abstract:*

Universality of geometric realization spaces for classes of combinatorial objects is a quite common phenomenon. Universality means essentially that for each semi-algebraic set there exists a combinatorial object of the given class such that its realization space is in some sense equivalent to the given semi-algebraic set.
The proofs always give some kind of encoding of semi-algebraic sets by combinatorial objects of the type under consideration.

After a brief overview of several known universality theorems I state a universality theorem for realization spaces of polyhedral maps (i.e. dissections of a closed 2-manifold into polygons) and give a fairly extensive sketch of the proof.

** Colloquium - 16:00**

### Dagmar Timmreck -
Freie Universität Berlin

### Obstructions to Geometric Realizability of Simplicial Surfaces through
Linking Numbers

*Abstract:*

In 1983 Brehm described a triangulation of the Möbius Strip that does not
admit a geometric realization in R^3.
His proof uses conditions on the linking numbers of pairs of polygonal
cycles on the surface to construct a contradiction.
We show how this approach can be systematically transferred to give
necessary conditions for the realizability of triangulated orientable
surfaces.

PhD defense lecture

Letzte Aktualisierung:
16.06.2014