Prof. Dr. Daniel Huson (University of Tübingen)
Abstract: This talk has four parts. In the first part - topology -, we recall the classification of two dimensions manifolds and orbifolds, and introduce their Conway notation. In the second part - geometry -, we discuss two-dimensional periodic tilings and their classification. In the third part - combinatorics -, we introduce Delaney-Dress symbols and indicate how they can be used to systematically enumerate periodic tilings. Finally, in the fourth part - algorithms and software -, we present Tegula (http://tegula.husonlab.org/), a new computer program that can be used the explore the “galaxy” of all 2.4 billion periodic tilings of the euclidean plane, sphere and hyperbolic plane, of low Dress-complexity. This is joint work with Olaf Delgado and Rüdiger Zeller.
