Graduiertenkolleg: Methods for Discrete Structures

Deutsche Forschungsgemeinschaft
faculty | junior-faculty | postdocs | students | associate students | former students | former associate students
locations | Term schedule | history
predoc-courses | schools | block-courses | workshops

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

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

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