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

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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.