The number of ramified coverings of the sphere by the double torus, and a general form for higher genera

An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the double torus, with elementary branch points and prescribed ramification type over infinity. Thus we are able to prove a conjecture of Graber and Pandharipande, giving a linear recurrence equation for the number of these coverings with no ramification over infinity. The general form of the series is conjectured for the number of these coverings by a surface of arbitrary genus that is at least two.Comment: 14pp.; revised version has two additional results in Section

Transitive factorizations of permutations and geometry

We give an account of our work on transitive factorizations of permutations. The work has had impact upon other areas of mathematics such as the enumeration of graph embeddings, random matrices, branched covers, and the moduli spaces of curves. Aspects of these seemingly unrelated areas are seen to be related in a unifying view from the perspective of algebraic combinatorics. At several points this work has intertwined with Richard Stanley's in significant ways.Comment: 12 pages, dedicated to Richard Stanley on the occasion of his 70th birthda

A proof of a conjecture for the number of ramified coverings of the sphere by the torus

An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the torus, with elementary branch points and prescribed ramification type over infinity. This proves a conjecture of Goulden, Jackson and Vainshtein for the explicit number of such coverings.Comment: 10 page

Integrated theory of hydroclimatic security, CLICO Working paper 13

This paper presents the updated conceptual framing of the CLICO research project, and evaluates the contribution of the CLICO research findings to theory on hydro-climatic security. We draw out the theoretical findings from twenty outputs of the five CLICO research work packages including twelve case studies in the Mediterranean, the Middle East and the Sahel region, where climate related water stresses threaten insecurity. We relate these findings to seven research questions. We then provide an updated conceptual framework of hydro-climatic security based on the findings and a summary of the key theoretical findings of the CLICO research. We find that climate change and water related stressors may exacerbate human insecurity either directly by adding to existing sources of human insecurity, or through maladaptive policies and interventions designed by governments in the name of adaptation to climate change. Factors that influence conflict situations and human security are multi-scalar and in most cases, more dependent on political, social and economic conditions rather than environmental factors. Conflict that is severe and prolonged is a significant driver of vulnerability to hydro-climate stressors. Cooperation, and more specifically coordination and communication between groups and institutions is seen as an important contributor to adaptive capacity. Without this divergent adaptation can occur, where one individual or group’s adaptation can reduce another’s adaptive capacity. Some debate exists as to the desirability of state intervention in adaptation and what constitutes adaptive capacity. Adaptation planning can be conflictive and present risks to human security when it fails to take into account different perspectives, values and knowledge bases and is open to manipulation by state actors. Case study evidence also supports arguments in favour of a balance between incrementalism and transformation, since transformational adaptation risks exacerbating some types of human insecurities

Uniform infinite planar triangulation and related time-reversed critical branching process

We establish a connection between the uniform infinite planar triangulation and some critical time-reversed branching process. This allows to find a scaling limit for the principal boundary component of a ball of radius R for large R (i.e. for a boundary component separating the ball from infinity). We show also that outside of R-ball a contour exists that has length linear in R.Comment: 27 pages, 5 figures, LaTe