Discrete quasiperiodic Schrodinger operators have been researched extensively over the past thirty years to produce a rather complete spectral analysis when the potential is defined by analytic functions. However, the nature of the spectral measures for less than $C^\infty$ regularity of the potential is largely unknown. We demonstrate that, with only minimal assumptions on the regularity of the potential, in the regime of positive Lyapunov exponents, the spectral measures are always of
Hausdorff dimension zero.

We will discuss systems of diffusion processes on the real line, in which the dynamics of every single process is determined by its rank in the entire particle system. Such systems arise in mathematical finance and statistical physics, and are related to heavy-traffic approximations of queueing networks. Motivated by the applications, we address questions about invariant distributions, convergence to equilibrium and concentration of measure for certain statistics, as well as hydrodynamic limits and large deviations for these particle systems. Parts of the talk are joint work with Amir Dembo, Tomoyuki Ichiba, Soumik Pal and Ofer Zeitouni

The adoption of new products which mainly spread through word-of-mouth (such as fax machines, skype, facebook, Ipad, etc.) is one of the key problems in Marketing research. Ideally, given the sales data of the first few months, one would like to be able to predict both the future sales and the overall market potential.

In this talk I will first present the classic Bass model and the agent-based approach for the adoption of new products. Then, I will present some recent analytic results on the effect of the social network on the adoption of new products.

This is joint work with Ro'i Gibori and Eitan Muller

We consider the problem of minimal Lagrangian immersions of disks into CH^2 which are equivariant to some surface group representation. We prove several results on existence and (non)uniqueness. The local parameterization of the immersion is given by the conformal structure on a closed surface and a holomorphic cubic differential on that conformal structure, hence of complex dimension 8g-8, where g>1 is the genus. This is a joint work with John Loftin and Marcello Lucia.