Non-integrality of some Steinberg modules

We prove that the Steinberg module of the special linear group of a quadratic imaginary number ring which is not Euclidean is not generated by integral apartments. Assuming the generalized Riemann hypothesis, this shows that the Steinberg module of a number ring is generated by integral apartments if and only if the ring is Euclidean. We also construct new cohomology classes in the top dimensional cohomology group of the special linear group of some quadratic imaginary number rings.Comment: 17 pages. To appear in Journal of Topolog

The Impact of French Opera in Nineteenth-Century New York: The New Orleans French Opera Company, 1827–1845

This dissertation examines the influence of French opera through the touring New Orleans French Opera Company’s summer seasons in early nineteenth-century New York City. In that burgeoning operatic environment, I provide an account of the company’s interaction with both resident and traveling opera companies, beginning with the visit of Manuel García’s company in 1825–26. The French Opera Company, which performed in 1827–33, 1843, and 1845, brought new approaches in performance practice and current opera repertoire to the New World. While Italian opera companies were sought after, I demonstrate that the works coming from Paris—either in French or in English translation—were both critically admired and more successful with audiences than the Italian works. In addition, I include details about the New York French community that demonstrate the influence of the Old World. Over a span of two decades, foreign-language opera in New York City began as a cultural experiment and ended in a flood of touring companies. The performances and reception of the New Orleans French Opera Company were integral in laying the foundation for future companies

Team-based Classroom Pedagogy Reframed: The Student Perspective

Postsecondary learning environments often utilize team-based pedagogical practices to challenge and support student learning outcomes. This manuscript presents the findings of a qualitative research study that analyzed the viewpoints and perceptions of group or team-based projects among undergraduate business students. Results identified five pro-team thematic perspectives of team learners’ views including better deliverables, increased ideas, improved learning experiences, reduced workload, and collective security. Responses from students who preferred to work autonomously resulted in three themes centered on self-sufficiency, social loafing, and schedule challenges. Two situational student responses were identified regarding how and why faculty should utilize group and team projects in consideration of individual efficiency and assignment objectives and outcomes conflicts. This study concludes with research-based recommendations for teaching, learning, and further research

On the generalized Bykovskii presentation of Steinberg modules

We study presentations of the virtual dualizing modules of special linear groups of number rings, the Steinberg modules. Bykovskii gave a presentation for the Steinberg modules of the integers, and our main result is a generalization of this presentation to the Gaussian integers and the Eisenstein integers. We also show that this generalization does not give a presentation for the Steinberg modules of several Euclidean number rings.Comment: Minor revisions based on referee's comments. Accepted for publication at IMR