09:00 to 09:55 Registration 09:55 to 10:00 David Wallace - welcome 10:00 to 11:00 D Thouless ([Washington])Localization, conduction, and superfluidity Localization of electrons characterizes the difference between an electrical insulator and a metallic conductor at low temperatures, and localization of atoms is one of the characteristics of a solid as opposed to a fluid. I discuss the suggestion made forty years ago that a quantum solid might be a supersolid with superfluid properties, and the recent experiments that show indications of superfluid properties in some solid helium samples. The behavior of the `center of mass' of a system with periodic boundary conditions in one direction sheds light on the possibility of reduced moment of inertia in a solid. It seems unlikely that supersolidity is a property of a good crystal, but it has been argued that networks of dislocations or of grain boundaries could support a superfluid within real crystals. INI 1 11:00 to 11:30 Coffee 11:30 to 12:30 S Kotani ([Osaka])On distribution of zeros of polynomials approximating exponential type entire functions We discuss the limiting behavior of the distribution of zeros of a certain class of polynomials when their degrees increase to infinity. A special case is polynomials which are obtained as a Maclaulin expansion of the exponential function and in this case,after a suitable normalization, the set of zeros converges to a smooth curve with a singulality at 1. Several generalizations will be presented. INI 1 12:30 to 13:30 Lunch at Wolfson Court 14:00 to 15:00 I Gornyi ([Forschungszentrum Karlsruhe])Anderson localization and electron-electron interaction I will discuss transport of interacting electrons in a low-dimensional disordered system at low temperature. In view of localization by disorder, the conductivity may only be non-zero due to electron-electron scattering. In this talk, I will review recent theoretical results on Anderson localization of interacting electrons. In particular, I will talk about Anderson localization and dephasing in strongly-correlated one-dimensional electron systems (disordered Luttinger liquids). The results I will describe were obtained in: I. V. Gornyi, A. D. Mirlin, D. G. Polyakov, Phys. Rev. Lett. 95, 046404 (2005); Phys. Rev. Lett. 95, 206603 (2005); Phys. Rev. B 75, 085421 (2007); D.A. Bagrets, I.V. Gornyi, A.D. Mirlin, D.G. Polyakov, arXiv:0804.4887; A.G. Yashenkin, I.V. Gornyi, A.D. Mirlin, D.G. Polyakov, arXiv:0808.1093. INI 1 15:00 to 15:30 Tea 15:30 to 16:30 HT Yau ([Harvard])Local semicircle law and complete delocalization for Wigner random matrices We consider $N\times N$ Hermitian random matrices with independent identical distributed entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order 1/N. Under suitable assumptions on the distribution of the single matrix element, we prove that, away from the spectral edges, the density of eigenvalues concentrates around the Wigner semicircle law on energy scales $\eta \gg N^{-1} (\log N)^8$. Up to the logarithmic factor, this is the smallest energy scale for which the semicircle law may be valid. We also prove that for all eigenvalues away from the spectral edges, the $\ell^\infty$-norm of the corresponding eigenvectors is of order $O(N^{-1/2})$, modulo logarithmic corrections. The upper bound $O(N^{-1/2})$ implies that every eigenvector is completely delocalized, i.e., the maximum size of the components of the eigenvector is of the same order as their average size. INI 1 16:30 to 17:30 F Wegner ([Heidelberg])Cell model for scaling near the mobility edgeSession: Rothschild Visiting Professor: Professor Juerg Froehlich On the basis of real-space renormalization (Z. Physik B25 (1976) 327) descriptive arguments for scaling at the mobility edge are given. Although these arguments are rather old, most of them are in qualitative agreement with today's knowledge on the behaviour around the mobility edge (non-linear sigma-model and renormalization). INI 1 17:30 to 18:30 Welcome Wine Reception 18:45 to 19:30 Dinner at Wolfson Court (Residents Only)