Undergraduate Seminar: "Gauss sums, Root Systems, and computing Whittaker Coefficients"

Abstract: Gauss sums are exponential sums which arise in the study of Fourier coefficients of automorphic forms and are number-theoretic in flavor. Root systems are highly symmetric structures which arise in the representation theory of Matrix groups and classification theory of semisimple Lie algebras. Together, we show how these two concepts are used in computing Whittaker Coefficients of automorphic forms. The talk will be hands-on and focussed on concrete examples. This is based on joint work with Swapnil Garg, Frank Lu, and Siki Wang at the UMN Math REU.

Host: Adeli Hutton