The spectral gluing theorem revisited

We strengthen the gluing theorem occurring on the spectral side of the geometric Langlands conjecture. While the latter embeds $IndCoh_N(LS_G)$ into a category glued out of 'Fourier coefficients' parametrized by standard parabolics, our refinement explicitly identifies the essential image of such embedding

The center of the categorified ring of differential operators

Let \Y be a derived algebraic stack satisfying some mild conditions. The purpose of this paper is three-fold. First, we introduce and study H(\Y), a monoidal DG category that might be regarded as a categorification of the ring of differential operators on \Y. When \Y = \LS_G is the derived stack of G-local systems on a smooth projective curve, we expect H(\LS_G) to act on both sides of the geometric Langlands correspondence, compatibly with the conjectural Langlands functor. Second, we construct a novel theory of D-modules on derived algebraic stacks. Contrarily to usual D-modules, this new theory, to be denoted by D^{der}, is sensitive to the derived structure. Third, we identify the Drinfeld center of H(\Y) with D^{der}(L\Y), the DG category of D^{der}-modules on the loop stack of \Y.Comment: To appear in J. Eur. Math. Soc. (JEMS

Loop group actions on categories and Whittaker invariants

We develop some aspects of the theory of $D$-modules on ind-schemes of pro-finite type. These notions are used to define $D$-modules on (algebraic) loop groups and, consequently, actions of loop groups on DG categories. Let $N$ be the maximal unipotent subgroup of a reductive group $G$. For a non-degenerate character $\chi: N(\!(t)\!) \to \mathbb{G}_a$ and a category $\mathcal{C}$ acted upon by $N(\!(t)\!)$, we define the category $\mathcal{C}^{N(\!(t)\!), \chi}$ of $(N(\!(t)\!), \chi)$-invariant objects, along with the coinvariant category $\mathcal{C}_{N(\!(t)\!), \chi}$. These are the Whittaker categories of $\mathcal{C}$, which are in general not equivalent. However, there is always a family of functors $\Theta_k: \mathcal{C}_{N(\!(t)\!), \chi} \to \mathcal{C}^{N(\!(t)\!), \chi}$, parametrized by $k \in \mathbb{Z}$. We conjecture that each $\Theta_k$ is an equivalence, provided that the $N(\!(t)\!)$-action on $\mathcal{C}$ extends to a $G(\!(t)\!)$-action. Using the Fourier-Deligne transform (adapted to Tate vector spaces), we prove this conjecture for $G= GL_n$ and show that the Whittaker categories can be obtained by taking invariants of $\mathcal{C}$ with respect to a very explicit pro-unipotent group subscheme (not ind-scheme) of $G(\!(t)\!)$

Good standing and cooperation

Indirect reciprocity is generally considered one of the leading mechanisms to explain how cooperation may emerge by natural selection. The basic intuition is that establishing a reputation of being a helpful individual increases the probability of being in turn helped. Two models have been proposed to describe how indirect reciprocity may work: the standing model (Sugden, 1986/2004) and the image-scoring model (Nowak and Sigmund, 1998a,b). Although there is evidence that the former model would perform better under a wide set of circumstances, it is often maintained that it requires individuals with an implausibly large capacity of processing recursive information. In this paper I argue that this is not actually the case. I then suggest that the information needed by the image-scoring model, under reasonable assumptions, may be sufficient for the standing model to work. Finally I emphasize that even if the hypothesis of indirect reciprocity is unable to give a fair account of the ecological bases of cooperation, it has inspired a deal of research precious to social sciences.Cooperation, Indirect reciprocity, Good standing, Image-Scoring.

Differences in IQ predict Italian North-South differences in (among other things) income: a comment

I provide a discourse on the article by Prof. Lynn (2010), which suggests that differences in intelligence explain per capita income levels across the Italian regions. To emphasize that his article is affected by flaws leading to false conclusions. This is clear as soon as some basic principles underpinning any rigorous scientific analysis are employed to discuss his findings.IQ, Income, Education, Italy.

The emergence of reciprocally beneficial cooperation

This paper offers a new and robust model of the emergence and persistence of cooperation. In the model, interactions are anonymous, the population is well-mixed, and the evolutionary process selects strategies according to material payoffs. The cooperation problem is modelled as a game similar to Prisoner’s Dilemma, but there is an outside option of nonparticipation and the payoff to mutual cooperation is stochastic; with positive probability, this payoff exceeds that from cheating against a cooperator. Under mild conditions, mutually beneficial cooperation occurs in equilibrium. This is possible because the non-participation option holds down the equilibrium frequency of cheating.Cooperation; voluntary participation; random payoffs.

Healthy, educated and wealthy : Is the welfare state really harmful for growth?

In this paper, we study how public and private expenditures in health and education affect economic growth by their influence on people's health, abilities, skills and knowledge. We consider a growth accounting framework in order to test whether welfare expenditures more than offset the efficiency losses caused by distortionary taxation, and whether the effects of public expenditure on economic growth differ from those of private expenditure. Our empirical analysis is based on a panel of 19 OECD countries observed between 1971 and 1998. The results are consistent with the hypothesis that the contribution of welfare expenditures more than compensates for the distortions caused by the tax system; and the estimated positive impact is stronger for health than for education. We also find some evidence that public expenditure influences GDP growth more than private expenditure.- En este trabajo se estudia cómo el gasto público y privado en sanidad y educación afectan el crecimiento económico a través de su influencia en la salud, las habilidades y el conocimiento de los individuos. Se considera un modelo de contabilidad del crecimiento para verificar si los beneficios de los gastos sociales compensan las pérdidas de eficiencia generadas por la imposición; y si los efectos del gasto público difieren de los efectos del gasto privado. El análisis empírico se basa en un panel de 19 países de la OCDE estudiados entre el periodo de 1971 y 1998. Los resultados son consistentes con la hipótesis que afirma que la contribución del gasto social compensa las distorsiones causadas por los impuestos; y que el impacto positivo del gasto en sanidad es superior al observado para la educación. También se observa que el gasto público tiene un efecto superior sobre el crecimiento del PIB que el gasto privad