On the Thurston-Kenyon program of characterizing expansions for nonperiodic self-affine tilings
Boris Solomyak, University of Washington

In his 1989 Lecture Notes, W. Thurston introduced the notion of self-similar tiling and stated the theorem characterizing expansions for such tilings in the plane as a certain class of algebraic integers (complex Perron numbers). Only the proof of necessity was given. R. Kenyon, in his 1990 Ph.D. thesis under the direction of Thurston, suggested a generalization to self-affine tilings in higher dimensions; however, his proof was incomplete. I will describe the recently completed (jointly with R. Kenyon) proof of necessity of the conjectured characterization in higher dimensions. The techniques developed for this proof are also useful in the study of spectral properties of tiling dynamical systems (work in progress with J.-Y. Lee).

Colloquium, Department of Mathematics, Rice University
March 20, 2008, 4-5PM, HB 227

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