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

Massive Degeneracy and Goldstone Bosons: A Challenge for the Light Cone

Wherein it is argued that the light front formalism has problems dealing with Goldstone symmetries. It is further argued that the notion that in hadron condensates can explain Goldstone phenomena is false.Comment: 7 pages, 5 figures, Invited Talk at Light Cone 2010, Valencia Spai

Historical Roots of Regional Sentencing Variation, The Symposium

I am a law professor and a criminal defense lawyer, not a historian. It is with some trepidation that I stand before you to suggest that our very persistent regional sentencing variations have roots in the political struggles of Reformation England and the cultures of the subgroups that populated the first American colonies. I rely upon others for the historical proof, as you will see, but I think I do have standing to argue to you that we should consider whether or not there is room, even in federal sentencing, to account for deeply embedded regional variations in our basic conceptions of why and how we should punish. Aware as I am of the dangers of essentializing and the ugly history of regional variation in American penal practices, I still want to ask whether Pennsylvanians really should be expected to punish transgressors in exactly the same way as Virginians. I will suggest to you that perhaps we should respect a modicum of regional variation and not seek to eliminate every vestige of regional legal culture in America