Intersections on moduli spaces of curves

We present a new approach to perform calculations with the certain standard classes in cohomology of the moduli spaces of curves. It is based on an important lemma of Ionel relating the intersection theoriy of the moduli space of curves and that of the space of admissible coverings. As particular results, we obtain expressions of Hurwitz numbers in terms of the intersections in the tautological ring, expressions of the simplest intersection numbers in terms of Hurwitz numbers, an algorithm of calculation of certain correlators which are the subject of the Witten conjecture, an improved algorithm for intersections related to the Boussinesq hierarchy, expressions for the Hodge integrals over two-pointed ramification cycles, cut-and-join type equations for a large class of intersection numbers, etc.

Glacial geomorphology of the Altai and Western Sayan Mountains, Central Asia

In this article, we present a map of the glacial geomorphology of the Altai andWestern Sayan Mountains, covering an area of almost 600,000 km2. Although numerous studies provide evidence for restricted Pleistocene glaciations in this area, others have hypothesized the past existence of an extensive ice sheet. To provide a framework for accurate glacial reconstructions of the Altai and Western Sayan Mountains, we present a map at a scale of 1:1,000,000 based on a mapping from 30 m resolution ASTER DEM and 15 m/30 mresolution Landsat ETM+ satellite imagery. Four landform classes have been mapped: marginal moraines, glacial lineations, hummocky terrain, and glacial valleys. Our mapping reveals an abundance of glacial erosional and depositional landforms. The distribution of these glacial landforms indicates that the Altai and Western Sayan Mountains have experienced predominantly alpine-style glaciations, with some small ice caps centred on the higher mountain peaks. Large marginal moraine complexes mark glacial advances in intermontane basins. By tracing the outer limits of present-day glaciers, glacial valleys, and moraines, we estimate that the past glacier coverage have totalled to 65,000 km2 (10.9% of the mapped area), whereas present-day glacier coverage totals only 1300 km2 (0.2% of the mapped area). This demonstrates the usefulness of remote sensing techniques for mapping the glacial geomorphology in remote mountain areas and for quantifying the past glacier dimensions. The glacial geomorphological map presented here will be used for further detailed reconstructions of the paleoglaciology and paleoclimate of the region.