Keeping a Clean Heart (Chapter 7 of For Today: A Prayer When Life Gets Messy)

Excerpt: When I heard that some of the kids at school received an allowance, money their parents actually gave to them for no particular reason other than to do a few chores around the house, I could hardly believe it. It seemed too good to be true. I never received an allowance, and the idea of having some spending money of any kind was usually out of the question. Once in a while, my mother would give my brothers and me a quarter each to go to the municipal swimming pool if we hoed five rows of corn in the garden, but that was the extent of it. Honestly, we had a loving and supportive family life and there was always good food on the table and clean clothes in the closet, but there wasn\u27t any extra money for extravagances like allowances. We lived paycheck to paycheck, and my parents fretted far more than I knew about running out of money before the end of the month. So, I decided to earn my own spending money. At the age of thirteen, I became an independent businessman- peddling papers for the Saginaw News

Book Review: Eastern Orthodox Christianity and American Higher Education: Theological, Historical, and Contemporary Reflections

‘‘Over the last two decades the American academy has engaged in a wide-ranging discourse on faith and learning, Christianity and higher education. Among the Christian voices that have weighed in on these topics, Orthodox Christians are not merely underrepresented; they are not even represented at all. This is not because no one has cared to listen but because scholars of the Orthodox tradition have rarely participated in these conversations’’ (p. 1). So begins the introduction to this significant book, the culmination of a decade-long conversation first initiated with the support of the Lilly Endowment’s Program for the Theological Exploration of Vocation at Hellenic College. Truly, scholars of the Orthodox tradition have now joined the faith and learning conversation with passion and civility, to borrow a phrase from Parker Palmer

Deformations of polarized automorphic Galois representations and adjoint Selmer groups

We prove the vanishing of the geometric Bloch-Kato Selmer group for the adjoint representation of a Galois representation associated to regular algebraic polarized cuspidal automorphic representations under an assumption on the residual image. Using this, we deduce that the localization and completion of a certain universal deformation ring for the residual representation at the characteristic zero point induced from the automorphic representation is formally smooth of the correct dimension. We do this by employing the Taylor-Wiles-Kisin patching method together with Kisin's technique of analyzing the generic fibre of universal deformation rings. Along the way we give a characterization of smooth closed points on the generic fibre of Kisin's potentially semistable local deformation rings in terms of their Weil-Deligne representations.Comment: Added reference to work of Breuil-Hellmann-Schraen. Minor change in assumption (b) of Theorems C and 3.1.3. Added Theorem 3.2.3 and subsection 3.3. Corrected typos and incorporated suggestions of the referee. To appear in Duke Math.

Modularity of nearly ordinary 2-adic residually dihedral Galois representations

We prove modularity of some two dimensional, 2-adic Galois representations over totally real fields that are nearly ordinary and that are residually dihedral. We do this by employing the strategy of Skinner and Wiles, using Hida families, together with the 2-adic patching method of Khare and Wintenberger. As an application we deduce modularity of some elliptic curves over totally real fields that have good ordinary or multiplicative reduction at places above 2.Comment: 87 pages. Typos correcte

The Six Word Memoir as Teaching Tool

This exercise takes place on the final day of class in my Business Communication course. The semester has been devoted, largely, to the idea that the fewer words used in business communication, the better. I use Coco Chanel\u27s quote about accessories- Never add, always remove -as a guideline for composing and editing both writing and speech. The goal is to get students to realize that, in almost all business communication, less is more, especially in today\u27s business world where much communication takes place electronically. But students also come to realize that less is more work , and that concision and brevity are more difficult to come by than long, effusive communication

The limiting distribution for the number of symbol comparisons used by QuickSort is nondegenerate (extended abstract)

In a continuous-time setting, Fill (2010) proved, for a large class of probabilistic sources, that the number of symbol comparisons used by QuickSort, when centered by subtracting the mean and scaled by dividing by time, has a limiting distribution, but proved little about that limiting random variable Y -- not even that it is nondegenerate. We establish the nondegeneracy of Y. The proof is perhaps surprisingly difficult