Operator Algebras and Dynamics Seminar
Fall 2013
All talks are from 3:454:45 p.m. in the Seminar Room, unless otherwise specified.

Dec02

Global wellposedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusionEvelyn LunasinUSNATime: 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 paracalculus and paraproduct 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 streamfunction 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.

Nov25

Cocycles of strict AIflowsDr. Gernot GreschonigUniversity 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 socalled 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 11 extensions takes place within the original flow, while in general case of the Veech structure theorem the induction process yields an almost 11 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 Mackeyrange.

Nov22

The GottschalkHedlund Theorem. When is a cocycle a coboundary?
View Abstract
We will present the proof of GottschalkHedlund'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.

Nov15

Groupoid actions on fractafoldsProf. Marius IonescuColgate University

Nov04

Some probabilistic results using dynamicsProf. Yuri LimaUniversity of Maryland

Sep13

Generalizations of Voiculescu's noncommutative Weylvon Neumann theorem and some applicationsProf. Thierry GiordanoUniversity of OttawaTime: 01:00 AM

Aug30

Bimodules over Cartan MASAs, and Mercer's extension theoremProf. Vrej ZarikianUSNATime: 01:00 AM