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Mathematics Department

Operator Algebras and Dynamics Seminar

Fall 2013

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

  • Dec
    02
  • Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion
    Evelyn Lunasin
    USNA
    Time: 03:45 PM

    View Abstract

    Our result improves the previous work of Danchin and Paicu 2008 [Global existence results for the anisotropic Boussinesq system in dimension two, Math. Models Methods Appl. Sci. 21 (2011), no. 3, 421—457.] We require a weaker initial data to establish uniqueness and also do so using only elementary tools from Sobolev spaces, avoiding the use of para-calculus and para-product formula from harmonic analysis. To achieve this, we use a new approach of defining an auxiliary “stream function” associated with the density, analogous to the stream-function associated with the vorticity in the 2D incompressible Euler equations and then proceed using the techniques of Yudovich (1963) for proving uniqueness for the 2D incompressible Euler equations. This is joint work with A. Larios and E.S. Titi.
  • Nov
    25
  • Cocycles of strict AI-flows
    Dr. Gernot Greschonig
    University of Maryland

    View Abstract

    We will generalize a result on the structure of real skew product extensions of distal minimal compact metric flows for a class of point distal flows. These so-called strict AI systems can be represented by a simplified Veech tower. In this simplified Veech tower the (possibly) transfinite induction process of isometric and almost 1-1 extensions takes place within the original flow, while in general case of the Veech structure theorem the induction process yields an almost 1-1 extension of the original point distal flow. Under the condition that every point in the skew product extension of a minimal compact metric strict AI flow is recurrent, we can obtain results equivalent to the distal case. That is, the existence of minimal compact metric flow as a topological version of the Mackey-range.
  • Nov
    22
  • The Gottschalk-Hedlund Theorem. When is a cocycle a coboundary?

    View Abstract

    We will present the proof of Gottschalk-Hedlund's theorem giving a criterion for a cocycle of a dynamical system to be a coboundary. We will introduce many basic dynamical notions such as minimality, skew products, transitivity, etc. No prior knowledge of topological dynamics is assumed.
  • Nov
    04
  • Some probabilistic results using dynamics
    Prof. Yuri Lima
    University of Maryland
  • Sep
    13
  • Generalizations of Voiculescu's non-commutative Weyl-von Neumann theorem and some applications
    Prof. Thierry Giordano
    University of Ottawa
    Time: 01:00 AM
  • Aug
    30
  • Bimodules over Cartan MASAs, and Mercer's extension theorem
    Prof. Vrej Zarikian
    USNA
    Time: 01:00 AM
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