Supercharacters on abelian groups

10/14/2014 - 12:15pm
10/14/2014 - 1:10pm
Stephan Ramon Garcia (Pomona College)

The theory of supercharacters, which generalizes classical character theory, was recently developed in an axiomatic fashion by P. Diaconis and I.M. Isaacs, based upon earlier work of C. Andre. When this machinery is applied to abelian groups, a wide variety of applications emerge.   In particular, we develop a broad generalization of the discrete Fourier transform along with several combinatorial tools. This perspective illuminates several classes of exponential sums (e.g., Gauss, Kloosterman, and Ramanujan sums) that are of interest in number theory.  We also consider certain exponential sums that produce visually striking patterns of great complexity and subtlety. 


Mudd Science Library 126, Pomona College