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

Revisiting ERISA’s Church Plan Exemption After Advocate Health Care Network v. Stapleton

For much of the last forty years, ERISA’s church plan exemption has existed quietly without much fanfare. But increased litigation over the last five years has dragged the exemption into the spotlight. The litigation focuses on religiously affiliated hospital systems and whether their pension plans have been correctly classified as church plans exempt from ERISA. This Note examines the history behind the church plan exemption, including statutory modifications made in 1980 and the IRS’s longstanding interpretation of these changes, which precipitated the dispute at issue in the current wave of litigation. While the U.S. Supreme Court’s recent decision in Advocate Health Care Network v. Stapleton endorsed a broad interpretation of the scope of the church plan exemption, this Note argues that Congress should revisit the church plan exemption and implement a more balanced approach to granting and evaluating church plan status. A more robust evaluation of church plan applicants would strike a balance between pension participants’ concerns around plan funding and other ERISA protections, and the needs of good faith church plan operators with valid religious affiliations

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 The other two are based on connections techniques; one due to Ocneanu, and the other previously unpublished, although likely known to Haagerup.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

At a Crossroads: Pakistani College Students’ Perspectives on Service and Service-Learning

With its large youth population, high unemployment, and limited educational opportunities, Pakistan is at a crossroads. Service-learning is a new concept in Pakistan, and several universities have begun to incorporate service into their curricula—with varying degrees of success—as a means for bridging academia with pressing community concerns. This qualitative case study explored Pakistani college students’ perceptions of service and how service-learning was being developed at their university, and the challenges they had encountered. Findings revealed students’ desire for a relevant education that not only prepares them for productive careers, but also serves their communities; gaps between the realities of and aspirations for education; issues of empowerment; and the need to mitigate risks. Analysis of the findings revealed a tension—a “tragic gap” (Palmer, 2004)—between what is and what could be in relation to service-learning and civic engagement in Pakistan

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

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

Let's Talk About It! Subjective and Objective Disclosures to Social Robots

This study aims to test the viability of using social robots for eliciting rich disclosures from humans to identify their needs and emotional states. Self-disclosure has been studied in the psychological literature in many ways, addressing both peoples' subjective perceptions of their disclosures, as well as objective disclosures evaluating these via direct observation and analysis of verbal and written output. Here we are interested in how people disclose (non-sensitive) personal information to robots, in an aim to further understand the differences between one's subjective perceptions of disclosure compared to evidence of disclosure from the shared content. An experimental design is suggested for evaluating disclosure to social robots compared to humans and conversational agents. Initial results suggest that while people perceive they disclose more to humans than to humanoid social robots or conversational agents, no actual observed differences in the content of the disclosure emerges between the three agents

Building Long-Term Human–Robot Relationships: Examining Disclosure, Perception and Well-Being Across Time

While interactions with social robots are novel and exciting for many people, one concern is the extent to which people’s behavioural and emotional engagement might be sustained across time, since during initial interactions with a robot, its novelty is especially salient. This challenge is particularly noteworthy when considering interactions designed to support people’s well-being, with limited evidence (or empirical exploration) of social robots’ capacity to support people’s emotional health over time. Accordingly, our aim here was to examine how long-term repeated interactions with a social robot affect people’s self-disclosure behaviour toward the robot, their perceptions of the robot, and how such sustained interactions influence factors related to well-being. We conducted a mediated long-term online experiment with participants conversing with thesocial robot Pepper 10 times over 5 weeks. We found that people self-disclose increasingly more to a social robot over time, and report the robot to be more social and competent over time. Participants’ moods also improved after talking to the robot, and across sessions, they found the robot’s responses increasingly comforting as well as reported feeling less lonely. Finally, our results emphasize that when the discussion frame was supposedly more emotional (in this case, framing questions in the context of the COVID-19 pandemic), participants reported feeling lonelier and more stressed. These results set the stage forsituating social robots as conversational partners and provide crucial evidence for their potential inclusion in interventions supporting people’s emotional health through encouraging self-disclosure