Converse theorems for representations of general linear groups over finite fields

This talk will be about the representation theory of GLn(F), where F is a finite field of characteristic p. I will focus on the representation theory with coefficients in F_l where l is a prime number different from p. I will discuss a converse theorem, proven jointly with J. Bakeberg, M. Gerbelli-Gauthier, H. Goodson, G. Moss, and R. Zhang, that says that you can characterize such representations using an associated invariant called a gamma factor. Gamma factors were originally studied in the context of the Langlands program, and have proven to be a useful tool in the representation theory of p-adic groups. I will assume minimal background and try to give lots of motivation throughout.