Supercharacters and their super powers

Start: 01/29/2014 - 4:15pm
End  : 01/29/2014 - 5:15pm


Stephan Garcia, Pomona College


Abstract: 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. Andr ́e. 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. (Partially supported by NSF Grants DMS-1265973, DMS-1001614, and the Fletcher Jones Foundation)

Shanahan Center for Teaching and Learning, Shanahan B460 (basement level), Harvey Mudd College

Garcia.pdf108.66 KB

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