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.

该奖项全部或部分根据2021年美国救援计划法案（公法117-2）资助。PI Monteiro，Nariel被授予国家科学基金会数学和物理科学上升博士后研究奖学金（NSF MPS-Ascend），以开展与扩大STEM代表性不足的群体参与有关的研究和活动计划。Monteiro博士的奖学金支持题为“有限局部主理想环上的一般线性群的表示理论”的研究项目，在赞助科学家的指导下。主办机构的奖学金是加州大学，圣克鲁斯，和赞助科学家是博士罗伯特Boltje。PI计划构建复杂的表示一般线性群在一个有限的地方主要理想环和调查的相似性表示这样的群体在任意领域的积极特征，特别是模块化表示。这种研究的主要技术将是使用块理论和G-代数的一般研究，这已经成功地应用于PI在r = 2的情况下。PI计划调查这些结果的推广到其他代数群。PI还将把时间集中在PROMYS数学圈（PMC）中发挥领导作用，该计划旨在增加STEM领域代表性不足的学生的代表性。这包括开发数学内容，申请赠款以支持PMC，并帮助运行一个为期6周的夏季计划。基于他之前在鼓励和支持来自代表性不足和低收入群体的学生参与STEM领域的项目方面的经验，PI将参与各种推广，招聘和保留举措。该奖项反映了NSF的法定使命，并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，被认为值得支持。