Toshi Sunada (Tokyo)

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<I>Discrete Abel-Jacobi maps and Abel's theorem</I>

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ABSTRACT:

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A graph version of ``Albanese maps" introduced in the study of asymptotic
behaviors of random walks on crystal lattices turns out to be closely
related to the notion of discrete Abel-Jacobi maps in algebraic graph
theory via a discrete analogue of Abel's theorem. Torelli's theorem in the
graph setting established recently by Caproraso and Viviani is also
discussed. For an illustration, I will refer to a hypothetical crystal,
whose structure has been known since 1932 and was characterized by myself
as a ``diamond twin" in view of symmetry.