Siegel-Veech constants for strata of moduli spaces of quadratic differentials

We present an explicit formula relating volumes of strata of meromorphicquadratic differentials with at most simple poles on Riemann surfacesand counting functions of the number of flat cylinders filled by closedgeodesics in associated flat metric with singularities. This generalizes the resultof Athreya, Eskin and Zorich in genus 0 to higher genera.Comment: 46 pages, 18 figure

Siegel-Veech constants for strata of moduli spaces of quadratic differentials

46 pages, 18 figuresInternational audienceWe present an explicit formula relating volumes of strata of meromorphicquadratic differentials with at most simple poles on Riemann surfacesand counting functions of the number of flat cylinders filled by closedgeodesics in associated flat metric with singularities. This generalizes the resultof Athreya, Eskin and Zorich in genus 0 to higher genera

Volumes of strata of moduli spaces of quadratic differentials: getting explicit values

The volumes of strata of Abelian or quadratic differentials play an important role in the study of dynamics on flat surfaces, related to dynamics in polygonal billiards. This article reviews all known ways to compute volumes in the quadratic case and provides explicit values of volumes of the strata of meromorphic quadratic differentials with at most simple poles in all low dimensions.Comment: 43 pages, 13 figures. To appear in Ann. Inst. Fourier. arXiv admin note: text overlap with arXiv:1405.589

Essays on labor economics and public finance

Public policies are an important determinant of the welfare of individuals and the society at large. Careful evaluation of the impact of public policies on welfare is therefore imperative for our understanding of the positive and normative implications for these institutions. The three chapters of this thesis examine the welfare consequences of specific economic and political institutions. Chapters 1 and 2 study two distinct channels through which social housing, a common feature of developed countries, may impact the neighborhoods in which they are built and the labor market outcomes of their low income tenants. Chapter 1 is concerned with the effect of the provision of social housing on neighboring private ats. It assesses the spillovers of low-income tenants and the change in the composition of the housing stock that are to be expected from the provision of new social housing units. In particular, it uses the direct conversion of private rental flats into social units without any accompanying rehabilitation to identify the impact of the inflow into the neighborhood of low income tenants, separately from the effects of social housing on the quality of the existing housing stock. Chapter 2 shows that social housing influences the location of low income tenants, and that the neighborhood of social housing units may improve the labor market outcomes of the poorest tenants. I observe the relocation of welfare recipients through the selection process of social housing applicants in the city of Paris from 2001 to 2007. The institutional process acts as a conditional randomization device across residential areas in Paris. The empirical estimates outline that neighborhoods have weak short- and medium-run effects on the economic self-sufficiency of poor households. Chapter 3, by contrast, focuses on how regional migrations of unemployed workers may affect their job search prospect in Europe. Using a longitudinal sample of French unemployment spells, the empirical estimates outline positive migration effects on transitions from unemployment to employment that depends on the previous duration of the unemployment spells

Geometry of periodic regions on flat surfaces and associated Siegel-Veech constants

31 pages, 9 figures. The final publication is available at Springer via http://dx.doi.org/10.1007/s10711-014-0014-z.International audienceAn Abelian differential gives rise to a flat structure (translation surface) on the underlying Riemann surface. In some directions the directional flow on the flat surface may contain a periodic region that is made up of maximal cylinders filled by parallel geodesics of the same length. The growth rate of the number of such regions counted with weights, as a function of the length, is quadratic with a coefficient, called Siegel-Veech constant, that is shared by almost all translation surfaces in the ambient stratum. We evaluate various Siegel-Veech constants associated to the geometry of configurations of periodic cylinders and their area, and study extremal properties of such configurations in a fixed stratum and in all strata of a fixed genus

Pillowcase covers: counting Feynman-like graphs associated with quadratic differentials

We prove the quasimodularity of generating functions for counting pillowcase covers, with and without Siegel-Veech weight. Similar to prior work on torus covers, the proof is based on analyzing decompositions of half-translation surfaces into horizontal cylinders. It provides an alternative proof of the quasimodularity results of Eskin-Okounkov and a practical method to compute area Siegel-Veech constants. A main new technical tool is a quasi-polynomiality result for 2-orbifold Hurwitz numbers with completed cycles

Geographic Inequality of Access to Employment in France: an Investigation Based on Comprehensive Administrative Sources

We analyze geographic inequality of access to employment at a highly detailed geographic level - the municipality - across all of metropolitan France (mainland + Corsica), for two population groups: unemployed persons registered at the National Employment Agency (ANPE) and recipients of the guaranteed minimum income (RMI). Overall, we find highly pronounced inequality of employment access by municipality of residence. However, across large sections of metropolitan France, groups of contiguous municipalities offer uniformly low or high prospects of employment access. Divergences between localities remain wide when we neutralize inter-municipal differences in socio-demographic composition: this finding confirms the existence of a specific territorial effect. To explain it, we introduce theoretical determinants of spatial economy into the analysis. The location of economic activities and issues of physical distance from the workplace do indeed have a strong impact, but geographic inequality of employment access may also be due to residential-segregation and social-network effects.Spatial Economics, Geographic Inequality, Employment Access