MPS-Ascend: Representation Theory of General Linear Groups over Finite Local Principal Ideal Rings

MPS-Ascend：有限局部主理想环上的一般线性群表示论

• 批准号: 2213166
• 负责人: Nariel Monteiro
• 金额: $ 30万
• 依托单位: Monteiro, Nariel
• 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: 2022-10-01 至 2025-09-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2213166&HistoricalAwards=false
• 关键词: MPS; Ascend; Representation; Theory; General

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). PI Monteiro, Nariel 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 broaden participation by groups underrepresented in STEM. This fellowship to Dr. Monteiro supports the research project entitled "Representation Theory of General Linear Groups over Finite Local Principal Ideal Rings," under the mentorship of a sponsoring scientist. The host institution for the fellowship is the University of California, Santa Cruz, and the sponsoring scientist is Dr. Robert Boltje.The PI plans to construct complex representations of general linear groups over a finite local principal ideal ring and investigate similarities with representations of such groups over arbitrary fields of positive characteristic, particularly the modular representations. The primary technique for such study will be to use block theory and the general study of G-algebras, which has previously been applied successfully by the PI in the case r = 2. The PI plans to investigate generalizations of such results to other algebraic groups. The PI will also focus his time on playing a leadership role in PROMYS Math Circle (PMC), a program focused on increasing the representation of underrepresented students in STEM fields. This includes developing mathematical content, applying for grants to support PMC, and helping run a 6-week summer program. Building on his prior experience with programs to encourage and support the participation of students from underrepresented and low-income groups in the STEM field, the PI will engage in various outreach, recruitment, and retention initiatives.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.

该奖项是根据2021年《美国救援计划法》（公法117-2）全部或部分资助的。 Nariel的Pi Monteiro被授予国家科学基金会的数学和物理科学升级博士后研究奖学金（NSF MPS-ASCEND），以开展与STEM中代表性不足的团体扩大参与的研究和活动计划。在赞助科学家的指导下，与Monteiro博士的这一奖学金支持了题为“一般线性群体代表理论相对于有限的本地主要理想环的代表理论”。奖学金的主持机构是加利福尼亚大学圣克鲁斯分校，赞助科学家是罗伯特·博尔特杰（Robert Boltje）博士。PI计划在有限的本地主要理想环上构建通用线性群体的复杂表示，并调查了与此类群体相似的相似之处，而在派上的积极典型表现方面，尤其是模块化表示。该研究的主要技术是使用块理论和G-Algebras的一般研究，PI先前已在r = 2的情况下成功地应用了该研究。 PI还将集中精力在Promiss Math Circle（PMC）中扮演领导角色，该计划旨在增加STEM领域中代表不足的学生的代表。这包括开发数学内容，申请赠款以支持PMC，并帮助运行为期6周的夏季计划。在他先前在计划的经验的基础上，旨在鼓励和支持来自人为不足和低收入小组在STEM领域的学生的参与，PI将参与各种宣传，招聘和保留计划。该奖项反映了NSF的法定任务，并通过评估该基金会的知识绩效和广泛的影响来评估NSF的法定任务，并被认为是值得的。