On Thursday, October 13, 2016, Dr. Jonathan Farley, Assistant Professor of Mathematics at Morgan State University, will present a colloquium lecture on “Sums-of-Squares Identities via Cauchy’s Theorem”
A theorem of Hurwitz states essentially that the product of a sum of n squares with a sum of n squares is a sum of n squares if and only if n=1,2,4, or 8. For instance, (a^2 + b^2)(A^2 + B^2) = (aA+bB)^2 + (aB-bA)^2. We prove that such formulas with coefficients in Z exist only if n is a power of 2. Our proof is combinatorial, but we can no longer remember that proof, so we use an argument of Fausto Membrillo-Hernandez to finish off the proof via Cauchy’s theorem about groups whose orders are divisible by a prime.
This lecture will be held in 7800 York Road, Room 320 at 4:00pm-5:00 p.m.
