The Tate Conjecture for a family of surfaces of general type with p_g=q=1 and K^2=3

We prove a big monodromy result for a smooth family of complex algebraic surfaces of general type, with invariants p_g=q=1 and K^2=3, that has been introduced by Catanese and Ciliberto. This is accomplished via a careful study of degenerations. As corollaries, when a surface in this family is defined over a finitely generated extension of Q, we verify the semisimplicity and Tate conjectures for the Galois representation on the middle \ell-adic cohomology of the surface.Comment: 26 pages. Final versio

Compounded Disadvantage: Race, Incarceration, and Wage Growth

Based on 14-year panel data on ex-prisoners, this paper reports the impact of incarceration on future job prospects. Black men, in addition to facing greater risk of ending up in prison, are more negatively affected by imprisonment than white men. The expansion of the U.S. criminal justice system is therefore responsible for compounding the disadvantages of African Americans

A rank inequality for the Tate Conjecture over global function fields

We present an observation of Ramakrishnan concerning the Tate Conjecture for varieties over a global function field (i.e., the function field of a smooth projecture curve over a finite field), which was pointed out during a lecture given at the AIM's workshop on the Tate Conjecture in July 2007. The result is perhaps “known to the experts,” but we record it here, as it does not appear to be in print elsewhere. We use the global Langlands correspondence for the groups GL_n over global function fields, proved by Lafforgue [Chtoucas de Drinfeld et correspondance de Langlands, Invent. Math. 147 (2002) 1–241], along with an analytic result of Jacquet and Shalika [On Euler products and the classification of automorphic forms. I and II, Amer. J. Math. 103 (1981) 499–558, 777–815] on automorphic L-functions for GL_n. Specifically, we use these to show (see Theorem 2.1 below) that, for a prime ℓ ≠ char k, the dimension of the subspace spanned by the rational cycles of codimension m on our variety in its 2m-th ℓ-adic cohomology group (the so-called algebraic rank) is bounded above by the order of the pole at s=m+1 of the associated L-function (the so-called analytic rank). The interest in this result lies in the fact that, with the exception of some special instances like certain Shimura varieties and abelian varieties which are potentially CM type, the analogous result for varieties over number fields is still unknown in general, even for the case of divisors (m=1)

The secret life of 1/n: A journey far beyond the decimal point

The decimal expansions of the numbers 1/n (such as 1/3 = .03333..., 1/7 = 0.142857...) are most often viewed as tools for approximating quantities to a desired degree of accuracy. The aim of this exposition is to show how these modest expressions in fact have much more to offer, particularly in the case when the expansions are infinitely long. First we discuss how simply asking about the period (that is, the length of the repeating sequence of digits) of the decimal expansion of 1/n naturally leads to more sophisticated ideas from elementary number theory, as well as to unsolved mathematical problems. Then we describe a surprising theorem of K. Girstmair showing that the digits of the decimal expansion of 1/p, for certain primes p, secretly contain deep facts that have long delighted algebraic number theorists

Book of Job

But turn in the Book of Job to the fourth chapter and let\u27s now look at the earthly scene. We\u27ve really spent the last two days looking at the heavenly scene and looking at this cosmic conflict, this test, this contest that is taking place in heaven. And you really do not understand the drama of the Book of Job unless you recognize that there is this heavenly scene that takes place in the first two chapters, which Job knows nothing about. Even when we come to the final chapter of the book, Job is still not informed of what all has been happening and why it has been happening

Defending Liberal Education: Implications for Educational Policy

This thesis advocates for the inclusion of liberal education in discussions of the college and university missions and mandates in North America. It is conceived with the purpose of influencing policy thinking and generating the theory and ideas required for sound education policy decision making. Research into liberal education is a special and atypical kind of inquiry and requires innovative theoretical approaches. Liberal education is foremost a philosophical problem and requires philosophical approaches. The method used is, therefore, conceptual in nature and drawn from analytical philosophy. My research approaches liberal education conceptually in three ways: historically, philosophically, and politically. Historically, all explanations of liberal education remain partial, debatable, and fragmentary. Philosophically, liberal education brings into focus fundamental questions and problems with a universal significance. Liberal education is perhaps best characterized as an ongoing argument, discussion, and debate. Politically, liberal education is relevant to many of the challenges facing North American society today. Liberal education is civic in nature, aimed at producing responsible citizens able to contribute to democracy and the continuation of democratic institutions. The contribution to knowledge made by this research is the development of liberal education towards idealism and universality. Universality provides the meta-principle needed to ground the inclusion of liberal education in the missions and mandates of North American colleges and universities. The synthesis of the three conceptual approaches (i.e., historical, philosophical, and political) produces a new justification for liberal education, one based in objectivity and rationality as universal values. My argument is that the values of objectivity and rationality are the best explanation of the universalist understanding of liberal education and its processes and goals

Development of failure frequency, shelter and escape models for dense phase carbon dioxide pipelines

PhD ThesisCarbon Capture and Storage (CCS) is recognised as one of a suite of solutions required to reduce carbon dioxide (CO2) emissions into the atmosphere and prevent catastrophic global climate change. In CCS schemes, CO2 is captured from large scale industrial emitters and transported, predominantly by pipeline, to geological sites, such as depleted oil or gas fields or saline aquifers, where it is injected into the rock formation for storage. The requirement to develop a robust Quantitative Risk Assessment (QRA) methodology for high pressure CO2 pipelines has been recognised as critical to the implementation of CCS. Consequently, failure frequency and consequence models are required that are appropriate for high pressure CO2 pipelines. This thesis addresses key components from both the failure frequency and consequence parts of the QRA methodology development. On the failure frequency side, a predictive model to estimate the failure frequency of a high pressure CO2 pipeline due to third party external interference has been developed. The model has been validated for the design requirements of high pressure CO2 pipelines by showing that it is applicable to thick wall linepipe. Additional validation has been provided through comparison between model predictions, historical data and the existing industry standard failure frequency model, FFREQ. On the consequences side, models have been developed to describe the impact of CO2 on people sheltering inside buildings and those attempting to escape on foot, during a pipeline release event. The models have been coupled to the results of a dispersion analysis from a pipeline release under different environmental conditions to demonstrate how the consequence data required for input into the QRA can be determined. In each model both constant and changing external concentrations of CO2 have been considered and the toxic effects on people predicted. It has been shown that the models can be used to calculate safe distances in the event of a CO2 pipeline release.National Gri