On the Arithmetic Fundamental Lemma in the minuscule case

The arithmetic fundamental lemma conjecture of the third author connects the derivative of an orbital integral on a symmetric space with an intersection number on a formal moduli space of $p$-divisible groups of Picard type. It arises in the relative trace formula approach to the arithmetic Gan-Gross-Prasad conjecture. We prove this conjecture in the minuscule case.Comment: Referee's comments incorporated; in particular, the existence of frames for using the theory of displays in the proofs of Theorems 9.4 and 9.5 is clarified. To appear in Compositio Mat

Human Capital Investment with Competitive Labor Search

We study human capital accumulation in an environment of competitive search. Given that unemployed workers can default on their education loans, skilled individuals with a larger debt burden prefer riskier but better paid careers than is socially desirable. A higher level of employment risk in turn depresses the skill premium and the incentives to invest in education. The equilibrium allocation is characterized by too much unemployment, underinvestment by the poor, and too little investment in skill-intensive technologies. A public education system funded by graduate taxes can restore efficiency. More generally, differences in education funding can account for cross-country variations in wage inequality.directed search, investment, education finance

Thermal spin injection and interface insensitivity in permalloy/aluminum metallic non-local spin valves

We present measurements of thermal and electrical spin injection in nanoscale metallic non-local spin valve (NLSV) structures. Informed by measurements of the Seebeck coefficient and thermal conductivity of representative films made using a micromachined Si-N thermal isolation platform, we use simple analytical and finite element thermal models to determine limits on the thermal gradient driving thermal spin injection and calculate the spin dependent Seebeck coefficient to be $-0.5\ \mu\mathrm{V}/\mathrm{K}< S_{s}<-1.3\ \mu\mathrm{V}/\mathrm{K}$. This is comparable in terms of the fraction of the absolute Seebeck coefficient to previous results, despite dramatically smaller electrical spin injection signals. Since the small electrical spin signals are likely caused by interfacial effects, we conclude that thermal spin injection is less sensitive to the FM/NM interface, and possibly benefits from a layer of oxidized ferromagnet, which further stimulates interest in thermal spin injection for applications in sensors and pure spin current sources