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- Department of Mathematics
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- Sunil Chebolu (Illinois State University)
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- General Events - Department of Mathematics
Speaker: Sunil Chebolu (Illinois State University)
Title: Mobius equivariant maps between fields
Abstract: Inspired by the classical Cauchy functional equation, we study the following problem: given a field F, classify all functions f from F to F that satisfy f((x + y)/(x − y)) = (f(x) + f(y))/(f(x) − f(y)) for all x ≠ y in F.
We give a complete solution to this problem and, more generally, classify all maps that are equivariant with respect to a Mobius transformation of the form (ax + by)/(cx + dy) on any field. Our results yield a new characterization of the field with five elements and the introduction of a novel group of transformations on a field that contains the automorphism group as a subgroup. This is joint work with Jonathan Love, Apoorva Khare, Anindya Sen, and Akaki Tikaradze.