Mathematics Department

Operator Algebras and Dynamics Seminar

Spring 2015

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

  • Feb
    27
  • The Unique Pseudo-Expectation Property for C*-Inclusions. II
    Time: 03:45 PM

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    Continuation of last week's lecture.
  • Feb
    20
  • The Unique Pseudo-Expectation Property for C*-Inclusions
    Time: 03:45 PM

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    A pseudo-expectation for a C*-inclusion (C,D) is a generalization of a conditional expectation. Whereas (C,D) may not have any conditional expectations, it must have at least one pseudo-expectation. One would expect the existence of a unique pseudo-expectation for (C,D) to be related to structural properties of the inclusion. In this talk, based on recent joint work with David Pitts, we investigate the unique pseudo-expectation property for C*-inclusions (C,D). After formally defining the property, we present some general results about it, in particular an order-theoretic characterization when D is abelian. Then we provide a number of examples of C*-inclusions with the unique pseudo-expectation property. Of special interest are the cases of abelian inclusions and W*-inclusions. Finally we relate the unique pseudo-expectation property to other properties of C*-inclusions, particularly norming in the sense of Pop, Sinclair, and Smith.
  • Jan
    16
  • Inverse limits and strange attractors
    Piotr Oprocha
    AGH University of Science and Technology, Krakow, Poland

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    In 1990 Barge and Martin presented a method of construction of global attractors of planar homeomorphisms in terms of inverse limits. This technique can also be extended to obtain attractors arising as inverse limits of degree one map of the circle. That way we can obtain attractors with very strange topological structure, such as pseudoarc or pseudocircle. In this talk we are going to survey some known results on dynamics on various types of continua that can be obtained as attractors. We are also going to mention some examples of maps on these spaces that cannot be constructed as shift homeomorphisms on inverse limit and present a few open problems that arise. At the end we are going to present recent results obtained jointly with Jan Boro\'nski. Among others we are going to explain how to obtain a pseudocircle as an attractor of map on a tori with a non-unique rotation vector on it. We will also comment on entropy and other dynamical properties of attractors obtained by this technique.
  • Jan
    09
  • On the simplicity of twisted k-graph C*-algebras
    Prof. Alex Kumjian
    University of Nevada

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    Let $\Lambda$ be a row-finite k-graph with no sources. It is well known that $C^*(\Lambda)$ is simple iff $\Lambda$ is aperiodic and cofinal. Given a categorical 2-cocycle c with vaues in $\mathbb{T}$ one may form the twisted k-graph C*-algebra, $C^*(\Lambda, c)$ . We use groupoid techiniques to characterize the simplicity of $C^*(\Lambda, c)$ generalizing recent work of Sims, Whitehead and Whittaker.
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