The Ore condition, affiliated operators, and the lamplighter group

Let G be the wreath product of Z and Z/2, the so called lamplighter group and k a commutative ring. We show that kG does not have a classical ring of quotients (i.e. does not satisfy the Ore condition). This answers a Kourovka notebook problem. Assume that kG is contained in a ring R in which the element 1-x is invertible, with x a generator of Z considered as subset of G. Then R is not flat over kG. If k is the field of complex numbers, this applies in particular to the algebra UG of unbounded operators affiliated to the group von Neumann algebra of G. We present two proofs of these results. The second one is due to Warren Dicks, who, having seen our argument, found a much simpler and more elementary proof, which at the same time yielded a more general result than we had originally proved. Nevertheless, we present both proofs here, in the hope that the original arguments might be of use in some other context not yet known to us.Comment: LaTex2e, 7 pages. Added a new proof of the main result (due to Warren Dicks) which is shorter, easier and more elementary, and at the same time yields a slightly more general result. Additionally: misprints removed. to appear in Proceedings of "Higher dimensional manifold theory", Conference at ICTP Trieste 200

The strong Novikov conjecture for low degree cohomology

We show that for each discrete group G, the rational assembly map K_*(BG) \otimes Q \to K_*(C*_{max} G) \otimes \Q is injective on classes dual to the subring generated by cohomology classes of degree at most 2 (identifying rational K-homology and homology via the Chern character). Our result implies homotopy invariance of higher signatures associated to these cohomology classes. This consequence was first established by Connes-Gromov-Moscovici and Mathai. Our approach is based on the construction of flat twisting bundles out of sequences of almost flat bundles as first described in our previous work. In contrast to the argument of Mathai, our approach is independent of (and indeed gives a new proof of) the result of Hilsum-Skandalis on the homotopy invariance of the index of the signature operator twisted with bundles of small curvature.Comment: 11 page

On a conjecture of Atiyah

In this note we explain how the computation of the spectrum of the lamplighter group from \cite{Grigorchuk-Zuk(2000)} yields a counterexample to a strong version of the Atiyah conjectures about the range of $L^2$-Betti numbers of closed manifolds.Comment: 8 pages, A4 pape

Career Funneling, Perceptions of Success, and Their Impact on College Students at Scripps, Pitzer, and Claremont McKenna Colleges

The U.S. News top college ranking lists have created a narrowing definition of collegiate and career success. Students are told an elite education is the ticket to a successful life, one filled with a high achieving career, meaning, and happiness. Through peer, familial, and media interfaces students are inundated with societal definitions of success such as fame, wealth, and status. Socialization primes adolescents to work towards these goals. This idealized type of success is only accessible to a select few, leading to dissatisfaction and creating pressures on students to work towards their college admission at early ages. This thesis examines the pressures elite college students face to become successful before, during, and after graduation and how striving to become successful funnels students towards similar college and career goals at the top of ranking of lists. Original research is adapted from Amy Binder, Daniel Davis, and Nick Bloom’s article, “Career Funneling: How Elite Students Learn to Define and Desire ‘Prestigious’ Jobs” and conducted at the Claremont Colleges to research the definitions of success, career aspirations, pressures, and their influences

Distribution of lipids in non-lamellar phases of their mixtures

We consider a model of lipids in which a head group, characterized by its volume, is attached to two flexible tails of equal length. The phase diagram of the anhydrous lipid is obtained within self-consistent field theory, and displays, as a function of lipid architecture, a progression of phases: body-centered cubic, hexagonal, gyroid, and lamellar. We then examine mixtures of an inverted hexagonal forming lipid and a lamellar forming lipid. As the volume fractions of the two lipids vary, we find that inverted hexagonal, gyroid, or lamellar phases are formed. We demonstrate that the non-lamellar forming lipid is found preferentially at locations which are difficult for the lipid tails to reach. Variations in the volume fraction of each type of lipid tail are on the order of one to ten per cent within regions dominated by the tails. We also show that the variation in volume fraction is correlated qualitatively with the variation in mean curvature of the head-tail interface.Comment: 10 pages, 12 figures (better figures are available upon request), to appear in J. Chem. Phy

Following Strain-Induced Mosaicity Changes of Ferroelectric Thin Films by Ultrafast Reciprocal Space Mapping

We investigate coherent phonon propagation in a thin film of ferroelectric PbZr0.2Ti0.8O3 (PZT) by ultrafast x-ray diffraction (UXRD) experiments, which are analyzed as time-resolved reciprocal space mapping (RSM) in order to observe the in- and out-of-plane structural dynamics simultaneously. The mosaic structure of the PZT leads to a coupling of the excited out-of-plane expansion to in-plane lattice dynamics on a picosecond timescale, which is not observed for out-of-plane compression.Comment: 5 pages, 4 figure

Thermoelastic study of nanolayered structures using time-resolved x-ray diffraction at high repetition rate

We investigate the thermoelastic response of a nanolayered sample composed of a metallic SrRuO3 (SRO) electrode sandwiched between a ferroelectric Pb(Zr0.2Ti0.8)O3 (PZT) film with negative thermal expansion and a SrTiO3 substrate. SRO is rapidly heated by fs-laser pulses with 208 kHz repetition rate. Diffraction of x-ray pulses derived from a synchrotron measures the transient out-of-plane lattice constant c of all three materials simultaneously from 120 ps to 5 mus with a relative accuracy up to Delta c/c = 10^-6. The in-plane propagation of sound is essential for understanding the delayed out of plane expansion.Comment: 5 pages, 3 figure

Numerical resonances for Schottky surfaces via Lagrange-Chebyshev approximation

We present a numerical method to calculate resonances of Schottky surfaces based on Selberg theory, transfer operator techniques and Lagrange-Chebyshev approximation. This method is an alternative to the method based on periodic orbit expansion used previously in this context.Comment: 26 pages, 10 figures, v2: more references and details adde

Energy and Structure of Hard-Sphere Bose Gases in three and two dimensions

The energy and structure of dilute gases of hard spheres in three dimensions is discussed, together with some aspects of the corresponding 2D systems. A variational approach in the framework of the Hypernetted Chain Equations (HNC) is used starting from a Jastrow wavefunction that is optimized to produce the best two--body correlation factor with the appropriate long range. Relevant quantities describing static properties of the system are studied as a function of the gas parameter $x=\rho a^d$ where $\rho$, $a$ and $d$ are the density, $s$--wave scattering length of the potential and dimensionality of the space, respectively. The occurrence of a maximum in the radial distribution function and in the momentum distribution is a natural effect of the correlations when $x$ increases. Some aspects of the asymptotic behavior of the functions characterizing the structure of the systems are also investigated.Comment: Proceedings of the QFS2004 conference in Trento. To appear in JLT