Abstract. This paper presents some recent progress on the classification of the unitary genuine irreducible representations of the metaplectic group Mp(2n). Our focus will be on Langlands quotients of genuine minimal principal series; the main result is an embedding of the set of unitary parameters of such representations into the union of spherical unitary parameters for certain split orthogonal groups. The latter are known from work of D. Barbasch; hence we obtain the non-unitarity of a large (conjecturally complete) set of parameters for Langlands quotients of genuine principal series of Mp(2n).

Abstract. The aim of this paper is to give an exposition of recent progress on the determination of the unitarizable Langlands quotients of minimal principal series for reductive groups over the real or p-adic fields in characteristic 0.

Abstract. In this paper we formulate a conjecture about the unitary dual of the metaplectic group. We prove this conjecture for the case of Mp(4,R). The result is a strengthening, for this case, of the following result by the third author: any unitary representation of a real reductive Lie group with strongly regular infinitesimal character can be obtained by cohomological induction from a one dimensional representation. Strongly regular representations are those whose infinitesimal character is at least as regular as that of the trivial representation. We are extending the result to representations with omegaregular infinitesimal character: those whose infinitesimal character is at least as regular as that of the oscillator representation. The proof relies heavily on Parthasarathy's Dirac operator inequality. In one exception we explicitly calculate the signature of an intertwining operator to establish nonunitarity. Some of the results on intertwining operators presented in section 5.2 are joint work of Dan M. Barbasch and the first author.

Studies have demonstrated students’ resistance to active learning, despite evidence illustrating that their learning is improved relative to students in lectures. Specifically, while active learning and group work are effective at engaging students in their learning process, studies report that students’ perceptions of active learning approaches are not always positive. What remains underexplored is whether students’ perceptions of active learning improve with effective instructor facilitation and whether there exists differential perceptions between racially minoritized students and represented students. Here, we estimate students’ perceptions of effective instructor facilitation as the mediator in the relationship between active learning and perceptions of learning and perceived utility for class activities (task value). Then, we examine differences by racial identification. We collected classroom observation data to empirically categorize courses as active learning or lecture-based and surveyed 4,257 college students across 25 STEM classrooms at a research-intensive university. We first examined the relationship between active learning on student perceptions and found a negative relationship between active learning and perceptions of learning and task value for both racially minoritized students and represented students. Next, we assessed whether students’ perceptions of instructor effectiveness in facilitating group activities mediate these negative relationships. We found that, on average, students of all races were more likely to positively perceive instructor facilitation in active learning classes relative to lectures. In turn, the positive perceptions of instructor facilitation partially suppressed the negative relationship between active learning and perceptions of learning and task value. These results demonstrate that effective instructor facilitation can influence both students’ self-assessment of learning and perceived utility of the learning activities, and underscores the importance of developing pedagogical competence among college instructors.

High‐quality afterschool programs (ASPs) are opportunities to diversify the ways that Latinx youth from economically underprivileged communities experience STEM learning. Utilizing qualitative methods, based on the experiences and perspectives of low‐income Latinx middle school participants of a math enrichment ASP in Southern California, we identified four culturally responsive practices: (1) the promotion of an inclusive, safe, and respectful program climate, (2) engaging in personal conversations, (3) facilitating opportunities for mutual and math learning across diverse cultures and perspectives, and (4) the promotion of math and a range of social‐emotional skills across contexts. These practices helped youth feel more connected to the program, their peers, and program staff (college mentors); provided a platform for youth voice and contribution to the processes of teaching and learning; facilitated opportunities for skill development and practice across the different contexts of youth’s lives; interrelated with Latinx cultural values; and helped to promote youth’s engagement and math learning. Importantly, youth’s relationships with their mentors was a significant aspect of their experiences and perceptions of these practices. We argue that culturally responsive practices are necessary to achieve high‐quality programs and provide specific implications for how ASPs can implement them in the design and implementation of their programs.