Groupoids: unifying internal and external symmetry

The aim of this paper is to explain, mostly through examples, what groupoids are and how they describe symmetry. We will begin with elementary examples, with discrete symmetry, and end with examples in the differentiable setting which involve Lie groupoids and their corresponding infinitesimal objects, Lie algebroids.Comment: 18 page

Hilbert modular forms with prescribed ramification

Let $K$ be a totally real field. In this article we present an asymptotic formula for the number of Hilbert modular cusp forms $f$ with given ramification at every place $v$ of $K$. When $v$ is an infinite place, this means specifying the weight of $f$ at $k$, and when $v$ is finite, this means specifying the restriction to inertia of the local Weil-Deligne representation attached to $f$ at $v$. Our formula shows that with essentially finitely many exceptions, the cusp forms of $K$ exhibit every possible sort of ramification behavior, thus generalizing a theorem of Khare and Prasad. From this fact we compute the minimal field over which a modular Jacobian becomes semi-stable.Comment: 30 pages, published versio

Discontinuous Tradition of Sentencing Discretion: Koon\u27s Failure to Recognize the Reshaping of Judicial Discretion under the Guidelines, The

Can a judge exercise discretion and follow the law? Some think it impossible, seeing discretion as the opposite of law. Others have harmonized the two ideas, viewing discretion as the exercise of judgment according to and within the bounds of the law. Those who decry judicial discretion urge legislatures to enact more specific laws and leave less room for the vice of inconsistent results. Those who defend discretion would channel it to achieve the virtue of individualized justice. The tension between individualization and uniformity in the law is often unnecessarily heightened by an inadequate analysis of judicial discretion. The exercise of judicial discretion in federal criminal sentencing exemplifies the problems arising from those inadequate analyses. The Sentencing Reform Act of 1984 ( SRA ) dramatically altered federal criminal sentencing for the express purpose of controlling judicial discretion. Judges were once free to impose any sentence from probation to the statutory maximum and were not subject to appellate review regarding the length of that sentence. However, they are now bound by the Sentencing Guidelines 7 and subject to appellate review of the sentences they impose. Despite this dramatic change, or perhaps because of it, the Supreme Court has used the breadth and uncertainty of the concept of discretion to paper over the fundamental reallocation of sentencing power in an effort to buttress the limited authority judges retain to individualize sentences

CORE: Frustrated Magnets, Charge Fractionalization and QCD

I explain how to use a simple method to extract the physics of lattice Hamiltonian systems which are not easily analyzed by exact or other numerical methods. I will then use this method to establish the relationship between QCD and a special class of generalized, highly frustrated anti-ferromagnets.Comment: Invited talk at Light-Cone 2004, 16 pages, 10 figure

Revenge of Mullaney v. Wilbur: United States v. Booker and the Reassertion of Judicial Limits on Legislative Power to Define Crimes, The

This article offers a historically grounded account of the twists and turns in the Supreme Court\u27s sentencing jurisprudence from the end of World War II to the Court\u27s stunning rejection of the Federal Sentencing Guidelines. The doctrinal shifts that have roiled this area of the law can best be understood as the Court\u27s effort to respond to the changing political and social landscape of crime in America. In the mid 1970\u27s, legislative activity in the criminal law was largely focused on Model Penal Code influenced recodification. In that era, the Supreme Court took power from an ascendant judiciary and gave it to legislators who did not seem disposed to exercise their authority too broadly. By the late 1990\u27s the tide had shifted and the Court turned sentencing doctrine on its head to take power over criminal law from legislative bodies inclined to push the limits of their power and transfer it back to a newly cautious judiciary. This article explores how that shift in power was informed by changing social and political conditions and was accomplished through doctrines regulating the Sixth Amendment right to trial