Supercharacters on abelian groups

01/29/2013 - 12:15pm
01/29/2013 - 1:10pm
Stephan Garcia (Pomona College)

The theory of supercharacters, which generalizes classical character theory, was recently developed in an axiomatic fashion by Diaconis and Isaacs, based upon earlier work of Andre. When this machinery is applied to abelian groups, a wide variety of applications emerge. We first discuss a generalization of the discrete Fourier transform (DFT) and its associated uncertainty principle. This perspective illuminates several classes of exponential sums (e.g., Gauss, Kloosterman, and Ramanujan sums) which are of interest in number theory. We also consider certain exponential sums which produce visually striking patterns, some of which appear related to the study of quasicrystals. (Partially supported by NSF Grant DMS-1001614, the Fletcher Jones Foundation, and Pomona College's SURP Program)

Millikan 208 (Pomona College)
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There will be a short organizational meeting for the ANTC seminar preceding the talk at 12:00 noon.