Tue, April 7, 2026
3:00 pm - 4:00 pm
Cockins Hall - CH228
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.