Fibonacci, golden ratio, and vector bundles

Abstract

There is a family of vector bundles over the moduli space of stable curves that, while first appearing in theoretical physics, has been an active topic of study for algebraic geometers since the 1990s. By computing the rank of the exceptional group $G_2$ case of these bundles in three different ways, we derive a family of summation formulas for Fibonacci numbers in terms of the golden ratio.