Gamma Factors for Mod Representations of Finite General Linear Groups

Explore the construction of gamma factors for mod 𝓁 representations of finite general linear groups in this 59-minute lecture by Ashwin Iyengar from the Hausdorff Center for Mathematics. Delve into the development of a converse theorem in this context, examining how the theorem fails for a "naïve" notion of gamma factor and discovering the solution through enlarged rings of coefficients. Investigate the relationship between this work and recent research by LiShotton on the infinite field analogue of "local Langlands in families." Learn about the collaborative efforts with J. Bakeberg, M. Gerbelli-Gauthier, G. Moss, H. Goodson, and R. Zhang in this mathematical exploration rooted in the tradition of Jacquet–Piatetski–Shapiro–Shalika's "Rankin-Selberg convolutions" paper.