Event

Talk
Geometric crystallography
Prof. Dr. Toshikazu Sunada (Meiji University/ Tokyo, Japan)
11 Nov 2008, 15:30

A crystal lattice (topological crystal) is defined to be an nfinite-fold cover over a finite graph. The graph theoretic version of Albanese maps is generalized in order to describe the most standard way to realize crystal lattices in space. We observe that the standard realization is characterized by a minimizing property of a certain energy functional. It is also pointed out that the standard realization comes up in a long time asymptotic behavior of random walks on a crystal lattice. This is used to show that the standard realization has maximal symmetry.

Related to:

• Toshikazu Sunada