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?

  Prof. Kostya Medynets

  USNA

  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

  15
• Groupoid actions on fractafolds

  Prof. Marius Ionescu

  Colgate University

  Abstract

• Nov

  04
• Some probabilistic results using dynamics

  Prof. Yuri Lima

  University of Maryland

  Abstract

• 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

  Abstract

• Aug

  30
• Bimodules over Cartan MASAs, and Mercer's extension theorem

  Prof. Vrej Zarikian

  USNA

  Time: 01:00 AM

  Abstract