Kazhdan's Property T and C*-algebras

Kazhdan's notion of property T has recently been imported to the C$^*$-world by Bekka. Our objective is to extend a well known fact to this realm; we show that a nuclear C$^*$-algebra with property T is finite dimensional (for all intents and purposes). Though the result is not surprising, the proof is significantly more complicated than the discrete group case.Comment: There was a mistake in the first draft, hence some preliminary results were removed. The proof of the main result, however, is unaffected. 5 page

Dynamos in Stellar Convection Zones: of Wreaths and Cycles

We live near a magnetic star whose cycles of activity are driven by dynamo action beneath the surface. In the solar convection zone, rotation couples with plasma motions to build highly organized magnetic fields that erupt at the surface and undergo relatively regular cycles of polarity reversal. Despite our proximity to the Sun, the nature of its dynamo remains elusive, but observations of other solar-type stars show that surface magnetism is a nearly ubiquitous feature. In recent time, numerical simulations of convection and dynamo action have taken tremendous strides forward. Global-scale organization and cyclic magnetism are being achieved by several groups in distinctly different solar and stellar simulations. Here I will talk about advances on the numerical front including wreath-building dynamos which may occupy stellar convection zones. I will discuss the interplay between the new simulations, various classes of mean-field models, and current and upcoming solar and stellar observations.Comment: 10 pages, 5 figures, a4 format; proceedings for SOHO 24/GONG 2010 conference: "A new era of seismology of the Sun and solar-like stars," Aix-en-Provence, France, June 27-July 4, 2010 (JPCS