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Jarkko Kari (University of Turku) "An Algebraic Geometric Approach to Multidimensional Symbolic Dynamics"
by Egor Pifagorov - Monday, 22 October 2018, 06:26 PM
 


ВНЕОЧЕРЕДНОЙ КОЛЛОКВИУМ ЛАБОРАТОРИИ ИМ. ЧЕБЫШЕВА

Вторник 23 октября 17:15 ауд. 14 (14-я линия В. О., 29)

Jarkko Kari (University of Turku)

"An Algebraic Geometric Approach to Multidimensional Symbolic Dynamics"

We study low complexity multidimensional words and subshifts using tools
of algebraic geometry. The low complexity assumption is that, for some
finite shape D, the word or the subshift has at most |D| distinct
patterns of shape D. We express words as multivariate formal power
series over integers and notice that the low complexity assumption
implies that there is an annihilating polynomial: a polynomial whose
formal product with the power series is zero. We prove that the word
must then be a sum of periodic words over integers, possibly with
unbounded values. As a specific application of the method we obtain an
asymptotic version of the well-known Nivat's conjecture: we can show
that a two-dimensional word that has low complexity with respect to
arbitrarily large rectangles D must be periodic.

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