Higher Laminations and Affine Buildings

We give a Thurston-like definition for laminations on higher Teichmuller spaces associated to a surface $S$ and a semi-simple group $G$ for $G-SL_m$ and $PGL_m$. The case $G=SL_2$ or $PGL_2$ corresponds to the classical theory of laminations. Our construction involves positive configurations of points in the affine building. We show that these laminations are parameterized by the tropical points of the spaces \X_{G,S} and \A_{G,S} of Fock and Goncharov. Finally, we explain how these laminations give a compactification of higher Teichmuller spaces.Comment: 46 page

Flowability of plane homeomorphisms

We describe necessary and sufficient conditions for an orientation preserving fixed point free planar homeomorphism that preserves the standard Reeb foliation to embed in a planar flow that leaves the foliation invariant.Comment: 20 pages, 3 figure

Zooming from Global to Local: A Multiscale RBF Approach

Because physical phenomena on Earth's surface occur on many different length scales, it makes sense when seeking an efficient approximation to start with a crude global approximation, and then make a sequence of corrections on finer and finer scales. It also makes sense eventually to seek fine scale features locally, rather than globally. In the present work, we start with a global multiscale radial basis function (RBF) approximation, based on a sequence of point sets with decreasing mesh norm, and a sequence of (spherical) radial basis functions with proportionally decreasing scale centered at the points. We then prove that we can "zoom in" on a region of particular interest, by carrying out further stages of multiscale refinement on a local region. The proof combines multiscale techniques for the sphere from Le Gia, Sloan and Wendland, SIAM J. Numer. Anal. 48 (2010) and Applied Comp. Harm. Anal. 32 (2012), with those for a bounded region in $\mathbb{R}^d$ from Wendland, Numer. Math. 116 (2012). The zooming in process can be continued indefinitely, since the condition numbers of matrices at the different scales remain bounded. A numerical example illustrates the process

Global Market Shocks and Poverty in Vietnam: The Case of Rice

World food prices have experienced dramatic increases in recent years. These "shocks" affect food importers and exporters alike. Vietnam is a major exporter of rice, and rice is also a key item in domestic production, employment and consumption. Accordingly, rice price shocks from the world market have general equilibrium impacts and as such, their implications for household welfare are not known ex ante. In this paper we first present a simple framework for understanding the direct and indirect welfare effects of a global market shock of this kind. Second, we quantify the transmission of the price shock from global indicator prices to domestic markets. Third, we then we use an applied general equilibrium (AGE) model to simulate the effects of domestic price changes in more detail. Fourth, a recursive mapping to a large nationally representative living standards survey permits us to identify in detail the ceteris paribus effects of the shock on household incomes and welfare. In this analysis, interregional and intersectoral adjustments in the labor market emerge as key channels transmitting the effects of global price shocks across sectors and among households.