The elliptic gamma function

The elliptic gamma function was (re)discovered in 1997 by Ruijsenaars; it gives rise to solutions of models in statistical / mathematical physics. It has a surprising number-theoretic appearance as demonstrated recently by Bergeron, Charollois and García. In parallel with the role of classical Jacobi theta form describing the class field for quadratic imaginary fields, the elliptic gamma function (conjecturally) does this task for cubic fields with a complex embedding. I will review some elements of this remarkable novel story by Bergeron-Charollois-García, including history and illustrative examples.