Counting and effective rigidity in algebra and geometry

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manifolds of bounded volume, the length sets (resp., the complex length sets) must disagree for a length that can be explicitly bounded as a function of volume. We also prove an effective version of a similar rigidity result established by the second author with Reid on a surface analog of the length spectrum for hyperbolic 3-manifolds. These effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras. To prove these effective rigidity results, we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest.Comment: v.2, 39 pages. To appear in Invent. Mat

Rural waste generation: a geographical survey at local scale

"The paper examines the per capita waste generation rates from from rural areas of Neamț County (Romania) using thematic cartography. Geographical approach of this issue is difficult because the lack of a geostatistic database at commune scale. Spatial analysis of waste indicators reveals several disparities between localities. Comparability of data between communes located in various geographical conditions must be carrefully made according to local waste management systems. Several dysfunctionalities are outlined in order to compare these results, on the one hand, between localities and on the one hand, between recent years. Geographical analysis of waste generation rates is imperative for a proper monitoring of this sector. Data from 2009, 2010 and 2012 shows that rural waste management is in a full process of change towards a more organized, stable and efficient system." (author's abstract