Multiplicity one theorems: the Archimedean case

Let $G$ be one of the classical Lie groups \GL_{n+1}(\R), \GL_{n+1}(\C), \oU(p,q+1), \oO(p,q+1), \oO_{n+1}(\C), \SO(p,q+1), \SO_{n+1}(\C), and let $G'$ be respectively the subgroup \GL_{n}(\R), \GL_{n}(\C), \oU(p,q), \oO(p,q), \oO_n(\C), \SO(p,q), \SO_n(\C), embedded in $G$ in the standard way. We show that every irreducible Casselman-Wallach representation of $G'$ occurs with multiplicity at most one in every irreducible Casselman-Wallach representation of $G$. Similar results are proved for the Jacobi groups \GL_{n}(\R)\ltimes \oH_{2n+1}(\R), \GL_{n}(\C)\ltimes \oH_{2n+1}(\C), \oU(p,q)\ltimes \oH_{2p+2q+1}(\R), \Sp_{2n}(\R)\ltimes \oH_{2n+1}(\R), \Sp_{2n}(\C)\ltimes \oH_{2n+1}(\C), with their respective subgroups \GL_{n}(\R), \GL_{n}(\C), \oU(p,q), \Sp_{2n}(\R), \Sp_{2n}(\C).Comment: To appear in Annals of Mathematic

Mathematics in Contemporary Society Chapter 1

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications. The textbook was posted in weekly installments: Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 1

Understanding Park Usership: An Examination of the Role of User Studies in Park Planning

This thesis examines the role of user studies in park planning. Cities spend millions of dollars maintaining, upgrading, and expanding urban park systems. Yet the physical design and upkeep of public spaces alone does not make for good parks; it is the users of public spaces that create vibrant, successful urban spaces. However, few park managers actually understand who the users of the public space are, in part because finding the answer is not considered a priority. Increasingly, planners have conducted regular user surveys as a method to understand park usership. While this process is challenging, data collected about park users collected through counts, surveys, interviews, observations, and many other methods provides extremely valuable information that cannot be learned through other methods. This information can guide decision making and inform park planning in many ways. Historical records establish that different forms of user analyses have long played a valuable, if underappreciated, role in understanding and shaping urban parks. This thesis uses visitor data collected at Brooklyn Bridge Park and interviews with planners to demonstrate how the information learned through user studies can be used to recognize important equity issues, design flaws, or conflicting uses, in addition to identifying possible solutions. The evidence suggests that user studies produce the most valuable findings when they are conducted regularly, combine several methods of data collection, and are used to supplement traditional methods of interacting with park constituents. While user studies can be extremely valuable in evaluating public spaces and guiding future improvements, lack of resources and inflexibility in the planning process impedes their value. Because each public space is unique, studies of usership are more appropriate at a park-specific level, although some findings may translate into generalizable knowledge. In order to make the most of user studies, the planning process needs to recognize not only the value of continuing evaluation, but the fact that evaluation can reveal unanticipated findings that require flexibility. Overall, performing regular studies of park usership is a valuable planning tool for all types of parks that should be prioritized and warrants public funding

Mathematics in Contemporary Society - Chapter 13 (Spring 2018)

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications

Mathematics in Contemporary Society - Chapter 7 (Spring 2018)

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications