Non-Divergence of Unipotent Flows on Quotients of Rank One Semisimple Groups

Let $G$ be a semisimple Lie group of rank $1$ and $\Gamma$ be a torsion free discrete subgroup of $G$. We show that in $G/\Gamma$, given $\epsilon>0$, any trajectory of a unipotent flow remains in the set of points with injectivity radius larger than $\delta$ for $1-\epsilon$ proportion of the time for some $\delta>0$. The result also holds for any finitely generated discrete subgroup $\Gamma$ and this generalizes Dani's quantitative nondivergence theorem \cite{D} for lattices of rank one semisimple groups. Furthermore, for a fixed $\epsilon>0$ there exists an injectivity radius $\delta$ such that for any unipotent trajectory $\{u_tx\}_{t\in [0,T]}$, either it spends at least $1-\epsilon$ proportion of the time in the set with injectivity radius larger than $\delta$ for all large $T>0$ or there exists a $\{u_t\}_{t\in\mathbb{R}}$-normalized abelian subgroup $L$ of $G$ which intersects $g\Gamma g^{-1}$ in a small covolume lattice. We also extend these results when $G$ is the product of rank-$1$ semisimple groups and $\Gamma$ a discrete subgroup of $G$ whose projection onto each nontrivial factor is torsion free.Comment: 23 page

Home Rule: Equitable Justice in Progressive Chicago and the Philippines

The evolution of the US justice system has been predominantly parsed as the rule of law and Atlantic crossings. This essay considers courts that ignored, disregarded, and opposed the law as the United States expanded across the Pacific. I track Progressive home rule enthusiasts who experimented with equity in Chicago and the Philippines, a former Spanish colony. Home rule was imbued with double meaning, signifying local self-governance and the parental governance of domestic dependents. Spanish and Anglo American courts have historically invoked equity, a Roman canonical heritage, to more effectively administer domestic dependents and others deemed lacking in full legal capacity, known as alieni juris or of another’s right. Thomas Aquinas described equity as the virtue of setting aside the fixed letter of the law to expediently secure substantive justice and the common good. In summary equity proceedings, juryless courts craft discretionary remedies according to the dictates of conscience and alternative legal traditions — such as natural law, local custom, or public policy — rather than the law’s letter. Equity was an extraordinary Anglo American legal remedy, an option only when common law remedies were unavailable. But the common law was notably deficient in the guardianship of alieni juris. Overturning narratives of equity’s early US demise, I document its persistent jurisdiction over quasi-sovereign populations, at home and abroad. Equity, I argue, is a fundamental attribute of US state power that has facilitated imperial expansion and transnational exchange

Vitamin A is essential for proper embryonic submandibular salivary gland growth.

Submandibular salivary glands (SMG) are important for the production of saliva. Salivary glands may be damaged by autoimmune disease, surgery, or radiation therapy. Retinoic acid (RA) is a signaling metabolite derived from Vitamin A that is essential for proper embryonic growth and development; specifically for cardiovascular, limb and craniofacial development. The goal of this study was to determine if there is a reproducible defect in the growth of SMGs in RA deficient mouse embryos compared to wild type. This study aims to characterize SMG growth in RA deficient embryos and determine if the growth could be stimulated by RA in a dose dependent manner. In addition, we hypothesized that there was a direct effect of the RA deficiency on SMG growth using an in vitro model. We examined Rdh10 mutant mouse embryos: which lack the enzyme retinol dehydrogenase necessary to produce RA. We examined the SMGs of wild type and Rdh10 mutant embryos by hematoxylin and eosin staining at various stages of gland development. We then completed whole mount antibody staining for the epithelium (E-cadherin) and nerve (TUJ), and compared the volumes of these glands. We also varied the dosage of all-trans-retinal (RAL), the intermediate in RA metabolism, supplementation to determine how this affects SMG growth. The mutant SMGs were approximately half the size of the wild type SMGs at both the early stage of gland development and further into development. With the higher dose of RAL, the mutant SMGs appeared more like the wild type, with branching and near normal SMG size. In order to see if RA directly affected SMG growth, wild type SMGs were cultured in vitro for up to 72 hours. SMGs treated with a synthetic Retinoic acid receptor (RAR) inhibitor (BMS 493) had less epithelium and branching compared to the control SMGs. Together, the results of these analyses demonstrate that RA directly affects SMG growth: specifically the epithelial growth and differentiation are influenced by the presence and dosage of RA

Court Review: Volume 41, Issue 2 - The Challenge of Funding State Courts in Tough Fiscal Times

It has been described as the worst state fiscal crisis since the end of World War II, with officials from across the country likening it to a “perfect storm,” “the Incredible Hulk of budget deficits,” and a “problem of historic proportions.” Beginning in 2001, almost every state experienced a deep fiscal crisis that placed funding of critical services in jeopardy and rendered many previously hallowed programs subject to draconian cuts, if not outright elimination. The fiscal crisis was particularly traumatic for court systems receiving all or a significant portion of their funding directly from state governments. In response to the fiscal crisis, courts curtailed operating hours, laid off employees, closed courthouses, eliminated funding for education programs, curtailed technology development, and abolished what were once thought to be inviolate, even sacrosanct programs. In some cases, state courts turned to local governments—who were facing their own budgetary problems—in an effort to “backfill” the reduction in state funds. In recent years, as state governments have replaced traditional local funding with state funding, the fate of the courts has become closely tied to the fiscal and political well-being of the state. Courts are being forced to compete for funding against more politically popular state services, such as education and public safety, or against seemingly out of control mandatory expenses, such as health care—often without much success. It would be easy to chalk the current fiscal crisis in the courts purely to state financing problems. Yet the financial crisis facing many state judiciaries is not simply a problem of cash flow or reduced revenues, and to paint it as such puts a far too simplistic spin on the matter. To be sure, a significant part of the crisis is rooted in economic factors. But to understand the true breadth of the problem, one must take account of the political factors affecting state court budgets. The crisis is defined by considerations that reflect not only money, but also the expanding influence of state judiciaries, offsetting concerns in some circles with “judicial activism,” and a seemingly growing and fundamental misunderstanding regarding the status and role of the courts in governing the nation. Donald L. Horowitz aptly described the current environment, which contrasts sharply with practices in England: The difference in the scope of judicial power in England and the United States should not be exaggerated. It is primarily a difference of emphasis. There have been periods of great passivity in America. But still the difference remains. What it has meant, in the main, is that American courts have been more open to new challenges, more willing to take on new tasks. This has encouraged others to push problems their way—so much so that no courts anywhere have greater responsibility for making public policy than the courts of the United States. Today, perhaps more so than at another time in the nation’s history, the courts are involved in policy making on such a broad range of matters that conflict with the other branches of government is inevitable and can involve budgetary considerations

Ohio Appellate Practice Before and After Polikoff: Are Things Really All That Much Clearer?

Perhaps no topic in Ohio appellate practice is more confusing than determining what constitutes a final, appealable order in a special proceeding. ... The ability of a litigant to obtain immediate review of a trial court order may hinge on an appellate court resolving the difficult question of whether the proceeding from which the order emanated constituted a special proceeding under Ohio law. The Supreme Court of Ohio, recognizing the difficulty in determining finality in a special proceeding has, like the appellate courts, struggled to articulate clearer guidelines and a more precise standard for resolving the question. The supreme court\u27s most recent attempt to provide guidance in this area is Polikoff v. Adam. However, rather than laying a foundation for clearer guidelines leading to a more consistent jurisprudence, the Polikoff decision further confuses the question of what is a special proceeding, forecloses examination of some types of orders requiring immediate appellate review because of their effect, and elevates the form of the underlying action over the substantive rights of the litigants affected by a trial court order