MPS-Ascend: The C*-Algebraic Mackey Bijection for Real Reductive Groups

MPS-Ascend：实数约简群的 C*-代数 Mackey 双射

• 批准号: 2213097
• 负责人: Angel Roman
• 金额: $ 30万
• 依托单位: Roman, Angel R
• 依托单位国家: 美国
• 项目类别: Fellowship Award
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-09-01 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2213097&HistoricalAwards=false
• 关键词: MPS; Ascend; Algebraic; Mackey; Bijection

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). PI Angel Roman is awarded a National Science Foundation Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowship (NSF MPS-Ascend) to conduct a program of research and activities related to broadening participation by groups underrepresented in STEM. This fellowship to Dr. Roman supports the research project entitled "The C*-Algebraic Mackey Bijection for Real Reductive Groups", under the mentorship of a sponsoring scientist. The host institution for the fellowship is Washington University in St. Louis, Missouri, and the sponsoring scientist is Dr. Xiang Tang. This project seeks to examine the Mackey bijection between tempered, irreducible unitary representations of a real reductive group and the unitary irreducible representations of its Cartan motion groups in greater detail through the theory of C*-algebras and through continuous fields of C*-algebras. Building on PI’s prior research, the PI will work with collaborators to better understand the cyclic homology of Harish-Chandra Schwartz algebras, an object of study in noncommutative geometry, using the embedding result and Mackey correspondence. The broadening participation activities are three-fold. The PI will collaborate with researchers in Puerto Rico to organize student-oriented conferences in Puerto Rico and help mentor Latin American students. Using the leadership development skills the PI used as a Taekwondo coach at Penn State, the PI will engage in graduate student and postdoctoral scholar's professional development through a working seminar on “Noncommutative geometry and Representation Theory.” Last but not the least, as a Hard-of-Hearing mathematician, the PI brings valuable insight to the issues faced by this community with transcription and captions for technical terms in mathematics. The PI will work with Gallaudet University, a premier university for the Deaf and Hard-of-Hearing with an undergraduate program in mathematics, in developing better resources.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项全部或部分由《2021 年美国救援计划法案》（公法 117-2）资助，PI Angel Roman 被授予美国国家科学基金会数学和物理科学提升博士后研究奖学金 (NSF MPS-Ascend)，以开展这项研究。一项与扩大 STEM 中代表性不足的群体的参与相关的研究和活动计划。Roman 博士的这项奖学金支持题为“C*-代数麦基双射实数”的研究项目。还原群”，在赞助科学家的指导下。该奖学金的主办机构是密苏里州圣路易斯的华盛顿大学，赞助科学家是唐向博士。该项目旨在研究调和的、不可约的之间的麦基双射通过 C* 代数理论和 C* 代数的连续域，更详细地描述了实数还原群的酉表示及其嘉当运动群的酉不可约表示。在 PI 之前的研究中，PI 将与合作者合作，利用嵌入结果和 Mackey 对应关系，更好地理解 Harish-Chandra Schwartz 代数的循环同调性，扩大参与活动的范围。将与波多黎各的研究人员合作，在波多黎各组织面向学生的会议，并利用 PI 在宾夕法尼亚州立大学担任跆拳道教练时使用的领导力发展技能来帮助指导拉丁美洲学生。 PI 将通过“非交换几何和表示论”工作研讨会参与研究生和博士后学者的专业发展。最后但并非最不重要的一点是，作为一名听力障碍数学家，PI 为该领域面临的问题带来了宝贵的见解。 PI 将与加劳德大学 (Gallaudet University) 合作开发更好的资源。加劳德大学是一所面向聋哑人和听力障碍人士开设数学本科课程的一流大学。通过使用基金会的智力价值和更广泛的影响审查标准进行评估，NSF 的法定使命被认为值得支持。