Mathematics Department

Operator Algebras and Dynamics Seminar

Fall 2015

All talks are from 3:45-4:45 p.m. in the Seminar room, unless otherwise specified.

  • Oct
  • A rigidity theorem for generalized odometers
    Kostya Medynets
    United States Naval Academy

    View Abstract

    We show that generalized odometers are continuously orbit equivalent if and only if the sequences of finite-index subgroups defining the systems are virtually isomorphic. For minimal equicontinuous $Z^d$-systems the continuous orbit equivalence implies that the acting groups have finite index subgroups (having the same index) whose actions are piecewise conjugate. This result extends M.~Boyle's flip-conjugacy theorem originally established for $\Z$-actions. As a corollary we obtain a dynamical classification of the restricted isomorphism between generalized Bunce-Deddens $C*$-algebras. We also show that the full group associated with a generalized odometer is amenable if and only if the acting group is amenable.
  • Oct
  • Sofic Shifts and Finite State Codes
    MIDN James Talisse
    Time: 03:45 PM

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    We present a necessary and sufficient condition for transforming a sofic shift into the full shift. In particular, if the entropy of the sofic shift is greater than or equal to the entropy of the full shift then such a transformation exists, which we call a finite-state code. Additionally a specific algorithm is developed for establishing finite-state codes. This has fundamental applications in data storage.
  • Sep
  • Dynamics of Some Substitution Systems
    Kelly B. Yancey
    University of Maryland, College Park
    Time: 03:45 PM

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    In this talk we will discuss substitution dynamical systems and some of their dynamical properties. Specifically we will talk about when they display the property of rigidity. Certain classes of interval exchange transformations will also be discussed in relation to substitutions. We will focus on 3-IETs.
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