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

Small Group Reading Instruction for English Language Learners in Grades 3-5

This project highlights best practices for small reading group instruction for third through fifth grade English language learners in the general education classroom. By completing a literature review, a journal article was developed to report the pros and cons of heterogeneous and homogeneous groupings for reading instruction. Data from the National Assessment for Educational Progress (NAEP) and the OSPI Report Card were used to discuss a need to raise student reading proficiency scores

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 The other two are based on connections techniques; one due to Ocneanu, and the other previously unpublished, although likely known to Haagerup.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

After the 1991 Gulf War ended, the Shiite population in southern Iraq and the Kurdish population in northern Iraq revolted against the Iraqi government... : deliberate attacks, imams from these mosques were providing medical treatment and shelter to injured civilians and insurgents...

. 3) Iraqi troops entered hospitals in Basrah and Karbala and summarily murdered any males between the age of 12 and 70. Iraqi troops also murdered, tortured, and raped medical personnel who had provided treatment to insurgents. 4) Ali Hassan Al Majid rounded up male civilians (of fighting age) and ordered them to drink petrol. After these men drank the petrol, Al Majid ordered his troops to fire or personally fired himself tracer bullets into the victims so that the petrol would ignite and the victim would explode. This tactic was used to intimidate people into offering information about insurgent activities. 5) Taha Yassin Ramadan allegedly ordered the Iraqi Air Force to load planes with bombs containing sarin nerve gas. These planes allegedly flew to Karbala and released their payloads over the city. The bombs did not detonate and no sarin was released into the city. Do any of these incidents constitute crimes within the jurisdiction of the Iraqi High Tribunal

Finding Humanity in Dystopia: Margaret Atwood\u27s The Handmaid\u27s Tale and Oryx and Crake

This thesis explores the relationship of humanity and literature in Margaret Atwood’s The Handmaid\u27s Tale and Oryx and Crake. Through personal narration, Offred tells the story of being a Handmaid in the Republic of Gilead, a totalitarian government in which language is forbidden. She struggles to remain human in a world that treats her as a reproductive machine. Offred’s experiences lead her to forbidden games with the Commander, an affair with the Commander’s guardian, and escape because of love and trust in a world void of emotion. In Oryx and Crake. Jimmy/Snowman thinks he is the last genuine human being left on the planet. He guards a genetically engineered people group called the Crakers. Jimmy/Snowman’s past with his best friend Crake and his lover Oryx provides the background for a story of loneliness and redemption as Jimmy seeks the answer to questions of tme humanity. Jimmy’s genuine humanity compares with the “humanity” of the Crakers, as Offred’s humanity frustrates the objective goals of the mechanical Republic of Gilead. The Handmaid\u27s Tale and Oryx and Crake align with Atwood’s larger thematic goals of promoting the protection of human rights and the environment. As Atwood makes her poignant stance, she also shows that literature is a powerful tool of humanity and that humanity flourishes through literature