Knot polynomial identities and quantum group coincidences

We construct link invariants using the $D_{2n}$ subfactor planar algebras, and use these to prove new identities relating certain specializations of colored Jones polynomials to specializations of other quantum knot polynomials. These identities can also be explained by coincidences between small modular categories involving the even parts of the $D_{2n}$ planar algebras. We discuss the origins of these coincidences, explaining the role of $SO$ level-rank duality, Kirby-Melvin symmetry, and properties of small Dynkin diagrams. One of these coincidences involves $G_2$ and does not appear to be related to level-rank duality.Comment: 50 pages, many figures (this version corrects a sign error in the G_2 braiding

Subfactors of index less than 5, part 2: triple points

We summarize the known obstructions to subfactors with principal graphs which begin with a triple point. One is based on Jones's quadratic tangles techniques, although we apply it in a novel way. The other two are based on connections techniques; one due to Ocneanu, and the other previously unpublished, although likely known to Haagerup. We then apply these obstructions to the classification of subfactors with index below 5. In particular, we eliminate three of the five families of possible principal graphs called "weeds" in the classification from arXiv:1007.1730.Comment: 28 pages, many figures. Completely revised from v1: many additional or stronger result

Changing the Story About Higher Education\u27s Public Purposes and Work: Land-Grants, Liberty, and the Little Country Theatre

Scott Peters, associate professor, Department of Education, Cornell University, examines the stories we tell about the history of higher education, using strategies of the humanities and the qualitative social sciences to illuminate competing accounts of the public mission of American land grant colleges. Specifically, he uncovers the historical relationship between culture and agriculture, building a bridge from Imagining America’s usual arena of the arts, humanities, and design to quite different kinds of work that are equally concerned with the layered meanings of place. His essay shows how the public mission of our colleges and universities has been—and is still being—negotiated through much-debated heroic, tragic, and prophetic meta-narratives. And as a leader of the movement for community engagement, he models precisely the kind of critical self-reflection and “public-regarding” practice that he hopes to find in the work of his own colleagues. Speaking directly to the producers of knowledge and culture who aim to become civic professionals, he offers a pragmatic strategy for hope

Subfactors of index exactly 5

We give the classification of subfactor planar algebras at index exactly 5. All the examples arise as standard invariants of subgroup subfactors. Some of the requisite uniqueness results come from work of Izumi in preparation. The non-existence results build upon the classification of subfactor planar algebras with index less than 5, with some additional analysis of special cases.Comment: 9 page

A Guide for Foreign Investors to Environmental Laws in the United States

This Article introduces, in some detail, the primary environmental rules and laws that are of special interest to potential foreign investors in the United States. The discussion includes examination of the Clean Air Act of 1988, The Federal Water Pollution and Control Act of 1972, and The Comprehensive Environmental Response, Compensation, and Liability Act of 1980 (CERCLA). The author also discusses specific laws that may apply to foreign investors, such as the regulation of underground storage tanks and asbestos laws. The author concludes that two types of costs exist for foreign investors in the United States: the cost of compliance with environmental legislation such as the Clean Air Act, and the cost of possible strict liability for expensive cleanups under CERCLA or the common law. The author recommends that foreign investors take whatever steps are available to identify and guard against environmental liability through pre-investment and contractual risk allocation

Induced pi-facial discrimination in the alkylation of chiral derivatives of glycine.

Part A. The alkylation trans 2-arylcyclohexyl hippurates with a series of electrophiles was examined. The reaction stereoselectivity varied from 46 to 81% depending on the steric and electronic nature of the electrophile when (Ar = phenyl). Higher stereoselectivity was observed when reacting electrophiles of increasing pi-character. When the chiral auxiliary contained a naphthyl group the stereoselectivity was \u3e80% for every electrophile used. Part B. The alkylation of the trans 2-phenylcyclohexylamide of methyl glycinate with a series of electrophiles was examined. Incorporation of the chiral auxiliary on the amino terminus of the amino acid appears to induce good stereoselectivity only when the electrophiles contain a point of unsaturation. The reaction stereoselectivity ranged from 21 to 80% depending on the electronic nature of the electrophiles. It is proposed that a pi-stacking interaction between the aromatic group on the auxiliary and the unsaturated electrophiles was responsible for the high stereochemical excess observed. Source: Masters Abstracts International, Volume: 39-02, page: 0514. Adviser: John M. McIntosh. Thesis (M.Sc.)--University of Windsor (Canada), 1999

Citizens Developing a Voice at the Table: A Story of Educational Organizing in Contemporary Extension Work

Diffusing and helping people to apply science-based information have long been viewed as the core tasks of Extension educators and specialists. But Extension work also includes a tradition of educational organizing that develops leadership, builds civic capacity, and facilitates learning through bringing people and resources together to identify, deliberate about, and act on important public issues and problems. This article draws from a practice story in contemporary Extension work in order to shed light on the dimensions and significance of educational organizing in today\u27s world

Rousing the People on the Land: The Roots of the Educational Organizing Tradition in Extension Work

Recent calls for engagement have land-grant institutions searching for ways to develop two-way partnerships between universities and communities for broad civic purposes. The renewal of a powerful but little understood tradition of educational organizing in Cooperative Extension work can help place Extension on the front lines of this important work. In this article, the author traces and discusses the roots of the tradition of educational organizing, shedding light on one of the most inspiring forgotten chapters of cooperative Extension history

The little desert? Some subfactors with index in the interval (5,3+\sqrt{5})

Progress on classifying small index subfactors has revealed an almost empty landscape. In this paper we give some evidence that this desert continues up to index 3 + \sqrt{5}. There are two known quantum-group subfactors with index in this interval, and we show that these subfactors are the only way to realize the corresponding principal graphs. One of these subfactors is 1-supertransitive, and we demonstrate that it is the only 1-supertransitive subfactor with index between 5 and 3 +\sqrt{5}. Computer evidence shows that any other subfactor in this interval would need to have rank at least 38. We prove our uniqueness results by showing that there is a unique flat connection on each graph. The result on 1-supertransitive subfactors is proved by an argument using intermediate subfactors, running the `odometer' from the FusionAtlas` Mathematica package and paying careful attention to dimensions.This research was funded through a grant. - ARC (DECRA award) and DARP