Operator Algebras and Dynamics Seminar
Spring 2015
All talks are from 3:454:45 p.m. in the Seminar room, unless otherwise specified.

Apr02

Symbolic Dynamics and Entropy via Conley Index TheoryProf. Sarah DayCollege of William and Mary
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Conley index theory, a generalization of Morse theory using algebraic topology, may be used in a computational framework to prove the existence of dynamics of various types. When searching for highly complicated dynamics, however, the Conley index may also become highly complicated and difficult to interpret. We present an automated approach to processing Conley index information for discretetime dynamical systems. This approach produces a topologically semiconjugate symbolic system whose entropy serves as a lower bound for the entropy of the system under study. Recent modifications of the original approach published in 2006 produce symbolic systems that capture more of the complexity encoded by the index, in some cases leading to substantial increases in computed lower bounds on system entropy. Sample results will be shown for the 2dimensional Henon map and the infinitedimensional KotSchaffer map. This is joint work with Rafael Frongillo.

Mar30

Multivariable dynamics and nonselfadjoint operator algebrasProf. Chris RamseyUniversity of Virginia
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Dynamical systems and operator algebras have had a love affair since the days of Murray and von Neumann. However, this has been a somewhat onesided relationship as much of the information encoded in the dynamics is lost in the crossed product. Enter a certain nonselfadjoint operator algebra called the semicrossed product. I aim to show that these semicrossed products are isomorphic if and only if their associated dynamical systems are conjugate.

Mar11

Equivalent operator categoriesProf. David ShermanUniversity of Virginia
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Leaving rigorous definitions to the talk, operator categories are natural classes that include C*algebras, operator systems, hereditary manifolds, operator algebras, Jordan operator algebras, etc. I will show how to associate the following features to any such category: an operator topology, a representation theory, and a convexity/dilation theory. It turns out that if one of these features agrees for a pair of categories, then all three do, in which case the categories are called equivalent. I will discuss some equivalences, along the way obtaining new observations about Arveson's hyperrigidity and maybe even triangles.

Feb27

The Unique PseudoExpectation Property for C*Inclusions. IIVrej ZarikianUSNATime: 03:45 PM
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Continuation of last week's lecture.

Feb20

The Unique PseudoExpectation Property for C*InclusionsVrej ZarikianUSNATime: 03:45 PM
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A pseudoexpectation 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 pseudoexpectation. One would expect the existence of a unique pseudoexpectation 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 pseudoexpectation property for C*inclusions (C,D). After formally defining the property, we present some general results about it, in particular an ordertheoretic characterization when D is abelian. Then we provide a number of examples of C*inclusions with the unique pseudoexpectation property. Of special interest are the cases of abelian inclusions and W*inclusions. Finally we relate the unique pseudoexpectation property to other properties of C*inclusions, particularly norming in the sense of Pop, Sinclair, and Smith.

Feb13

Irreducible Induced Representations of Fell Bundle C*algebras. IIIProf. Marius IonescuUSNA

Feb06

Irreducible Induced Representations of Fell Bundle C*algebras. II.

Jan23

Irreducible Induced Representations of Fell Bundle C*algebras

Jan16

Inverse limits and strange attractorsPiotr OprochaAGH 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 nonunique rotation vector on it. We will also comment on entropy and other dynamical properties of attractors obtained by this technique.

Jan09

On the simplicity of twisted kgraph C*algebrasProf. Alex KumjianUniversity of Nevada
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Let $\Lambda$ be a rowfinite kgraph with no sources. It is well known that $C^*(\Lambda)$ is simple iff $\Lambda$ is aperiodic and cofinal. Given a categorical 2cocycle c with vaues in $\mathbb{T}$ one may form the twisted kgraph 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.