Conjectures about discriminants of Hecke algebras at prime level

We study p-divisibility of discriminants of Hecke algebras associated to spaces of cusp forms of prime level. We make a precise conjecture about the indexes of Hecke algebras in their normalisation which implies (if true) the conjecture that there are no mod p congruences between non-conjugate newforms of weight 2 and level Gamma_0(p).Comment: To appear in ANTS 6 Proceeding

Sharp decay estimates for critical Dirac equations

We prove sharp pointwise decay estimates for critical Dirac equations on $\mathbb{R}^n$ with $n\geq 2$. They appear for instance in the study of critical Dirac equations on compact spin manifolds, describing blow-up profiles, and as effective equations in honeycomb structures. For the latter case, we find excited states with an explicit asymptotic behavior. Moreover, we provide some classification results both for ground states and for excited states.Comment: Final version to appear in Trans. Amer. Math. So

Credit unions and the common bond

Credit Unions are cooperative financial institutions specializing in the basic financial needs of certain groups of consumers. A distinguishing feature of credit unions is the legal requirement that members share a common bond. This organizing principle recently became the focus of national attention as the Supreme Court and the U.S. Congress took opposite sides in a controversy regarding the number of common bonds that could co-exist within the membership of a single credit union. Despite its importance, little research has been done into how common bonds affect how credit unions actually operate. We frame the issues with a simple theoretical model of credit-union formation and consolidation. To provide intuition into the flexibility of multiple-group credit unions in serving members, we simulate the model and present some comparative-static results. We then apply a semi-parametric empirical model to a large dataset drawn from federally chartered occupational credit unions in 1996 to investigate the effects of common bonds. Our results suggest that credit unions with multiple common bonds have higher participation rates than credit unions that are otherwise similar but whose membership shares a single common bond

Daily measurement of slow slip from low-frequency earthquakes is consistent with ordinary earthquake scaling.

Slow slip transients on faults can last from seconds to months and stitch together the earthquake cycle. However, no single geophysical instrument is able to observe the full range of slow slip because of bandwidth limitations. Here, we connect seismic and geodetic data from the Mexican subduction zone to explore an instrumental blind spot. We establish a calibration of the daily median amplitude of the seismically recorded low-frequency earthquakes to the daily geodetically recorded moment rate of previously established slow slip events. This calibration allows us to use the precise evolution of low-frequency earthquake activity to quantitatively measure the moment of smaller, subdaily slip events that are unresolvable by geodesy alone. The resulting inferred slow slip moments scale with duration and inter-event time like ordinary earthquakes. These new quantifications help connect slow and fast events in a broad spectrum of transient slip and suggest that slow slip events behave much like ordinary earthquakes

Corporate governance and corporate performance

National corporate-governance traditions are distinctive, deeply rooted, and difficult to change. Recent research points to a country's legal traditions and its stage of economic development as important determinants of corporate-governance institutions. Common-law countries tend to provide more explicit investor protections than civil-law countries. Richer countries tend to enforce corporate law more strictly. Broader and deeper financial markets emerge in the presence of strong investor protections, fostering more outside financing and better corporate financial performance. Corporate-governance systems also influence resident firms' capital structures and ownership structures. A broader perspective on corporate performance suggests that no country's system of corporate governance is without shortcomings, however.Corporations - Finance ; Corporations