Characterizing homomorphisms via Fourier analysis, by Prof. Leo Goldmakher, Williams College
Fri, September 27th, 2024
1:00 pm - 1:50 pm
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Characterizing homomorphisms via Fourier analysis, by Prof. Leo Goldmakher, Williams College, Friday September 27, North Science Building 015, Wachenheim, Faculty Seminar
Abstract: Suppose f is a function from the multiplicative group (mod p) to the nonzero complex numbers under multiplication. Is f a homomorphism? In very recent work (joint with Jonathan Bober) we found that—under some very mild hypotheses—f is a homomorphism if and only if the Fourier transform of f has magnitude 1 somewhere. An immediate consequence is a converse to a celebrated theorem of Gauss.
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