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

该奖项的全部或部分资金来自《2021年美国救援计划法案》(公法117-2)。Pi Monteiro，Nariel被授予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。这项给Monteiro博士的奖学金支持在一位赞助科学家的指导下进行的名为“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。该奖学金的主办机构是加州大学圣克鲁斯分校，赞助科学家是Robert Boltje博士。PI计划在有限局部主理想环上构造一般线性群的复杂表示，并研究此类群在具有正特征的任意域上的表示的相似性，特别是模表示。这种研究的主要技巧将是使用块论和G-代数的一般研究，在r=2的情况下，PI已经成功地应用了这一方法。PI计划研究这些结果在其他代数群上的推广。PI还将把他的时间集中在PROMYS Math Circle(PMC)中发挥领导作用，这是一个专注于增加STEM领域代表性不足的学生的计划。这包括开发数学内容，申请拨款支持PMC，以及帮助运营一个为期6周的暑期项目。根据他之前在鼓励和支持来自代表不足和低收入群体的学生参与STEM领域的计划方面的经验，PI将参与各种外展、招聘和保留计划。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.