Event

Talk
Discrete Abel-Jacobi maps and a diamond twin
Prof. Dr. Toshikazu Sunada (Meiji University/ Tokyo, Japan)
11 Nov 2008, 17:00

An Abel-Jacobi map in algebraic graph theory is a canonically defined harmonic function on vertices of a graph with values in a finite abelian group. This notion is a discrete analogue of Abel-Jacobi maps in algebraic geometry. One may also introduce an analogue of Albanese maps which are canonical harmonic maps of graphs as 1-dimensional cell complexes into flat tori. A discrete version of Abel's theorem tells, as it is the case in algebraic geometry, that these two notions are closely related. Not surprisingly, graph theoretic Albanese maps (and generalizations) turn out to be useful in geometric descriptions of crystals. For an illustration, we will treat the ``diamond twin" which has the same property of symmetry as the diamond crystal and has been pinned down in the study of random walks on crystal lattices.

Related to:

• Toshikazu Sunada