On the equidistribution of some Hodge loci

We prove the equidistribution of the Hodge locus for certain non-isotrivial, polarized variations of Hodge structure of weight $2$ with $h^{2,0}=1$ over complex, quasi-projective curves. Given some norm condition, we also give an asymptotic on the growth of the Hodge locus. In particular, this implies the equidistribution of elliptic fibrations in quasi-polarized, non-isotrivial families of $K3$ surfaces.Comment: 33 pages. To appear in Journal f\"ur die reine und angewandte Mathematik (Crelles Journal

Channels with Cooperation Links that May Be Absent

It is well known that cooperation between users in a communication network can lead to significant performance gains. A common assumption in past works is that all the users are aware of the resources available for cooperation, and know exactly to what extent these resources can be used. Unfortunately, in many modern communication networks the availability of cooperation links cannot be guaranteed a priori, due to the dynamic nature of the network. In this work a family of models is suggested where the cooperation links may or may not be present. Coding schemes are devised that exploit the cooperation links if they are present, and can still operate (although at reduced rates) if cooperation is not possible.Comment: Accepted for publication in the IEEE transaction on Information Theory, June 201

Skolem-Noether for nilpotent products

We consider the structure of groups and algebras that can be represented as automorphisms or derivations of distributive products -- which includes nonassociative rings, modules, forms, and commutation of groups and nonassociative loops. In many ways this is too broad to be possible, for instance even naive structure, such as inner automorphisms and derivations, are undefined for general bilinear maps. The appeal for working in this generality is broad applicability. We introduce fundamental structures and prove several results akin to ones in ring theory, including theorems of Morita and of Skolem-Noether type. Applications and examples are included.Comment: 29 pages, 2 figures, 1 tabl

Chiral Disorder and QCD Phase Transitions

If QCD is to undergo a second order phase transition, the light quark return probability is universal for large times at the critical point. We show that this behavior is distinct from the one expected at the mobility edge of a metal-insulator transition or a percolation transition in d$\leq 4$. Our results are accessible to current lattice QCD simulations.Comment: 5 pages RevTe

Public provision of private goods, self-selection and income tax avoidance

Several contributions in the optimal taxation literature have emphasized that, when individuals’ preferences are not separable between leisure and other goods, it is desirable to supplement a nonlinear income tax with public provision of private goods. Moreover, it has also been shown that the choice between a topping-up and an opting-out scheme depends on whether the publicly provided good is a complement or substitute with leisure, with opting-out (topping-up) being the preferred scheme for goods which are substitutes (complements)for labor. In this paper, using the self-selection approach to tax analysis, we revisit these results in the presence of tax avoidance, and investigate how public provision interacts with the agents’incentives to engage in tax avoidance. Three results are obtained. First, we show that tax dodging opportunities imply that non-separability between labor and other goods is neither a necessary nor a sufficient condition to make public provision of private goods a welfare-enhancing policy instrument. Second, we show how tax dodging opportunities limit the scope for using topping-up provision schemes as a redistributive device. Finally, we show that, for most of the public provision schemes previously analyzed in the literature, being a welfare-enhancing policy instrument goes hand in hand with weakening the agents’incentives to shelter income from the tax authority. However, we also point out an important exception to this pattern.optimal nonlinear income tax; public provision of private goods; tax avoidance