Colloquium: Tuesday, June 2 2pm. Speaker: Felix Pogorzelski (Technion). Title: Polygonal complexes and non-positive planar sectional curvature.

We study a notion of planar sectional curvature for polygonal complexes.

These complexes are endowed with a collection of certain planar subcomplexes.

The first part of the talk is devoted to a description of these objects.

After that, we discuss some geometric consequences of non-positive curvature such as Gromov-hyperbolicity and positive Cheeger constant.

If time permits, we draw a connection between non-positively curved geometry of the complex and the spectrum of the discrete Laplacian, the latter being defined as an operator on the faces of the complex.

Joint work with Matthias Keller (Jena) and Norbert Peyerimhoff (Durham).