Abstract: I will introduce a novel curvature flow, the Heterotic-Ricci flow, as the two-loop renormalization group flow of the Heterotic string common sector and study its three-dimensional compact solitons. The Heterotic-Ricci flow is a coupled curvature evolution flow, depending on a non-negative real parameter $\kappa$, for a complete Riemannian metric and a three-form $H$ on a manifold $M$. Its most salient feature is that it involves a term quadratic in the curvature tensor of a metric connection with skew-symmetric torsion $H$. When $\kappa = 0$ the Heterotic-Ricci flow reduces to the generalized Ricci flow and hence it can be understood as an extension of the latter via a higher order correction prescribed by string theory, whereas when $H = 0$ and $\kappa > 0$ the Heterotic-Ricci flow reduces to a constrained version of the RG-2 flow and hence it can be understood as a generalization of the latter via the introduction of the three-form $H$. Solutions of Heterotic supergravity with trivial gauge bundle, which we call Heterotic solitons, define a particular class of solitons for the Heterotic-Ricci flow. I will present a number of structural results for three-dimensional Heterotic solitons, providing the complete classification of three-dimensional strong Heterotic solitons as quotients of the Heisenberg group equipped with a left-invariant metric. Furthermore, I will prove that all Einstein three-dimensional Heterotic solitons have constant dilaton, leaving as open the construction of a Heterotic soliton with non-constant dilaton. In this direction, I will prove that Heterotic solitons with constant dilaton are rigid and therefore cannot be deformed into a soliton with non-constant dilaton. Work in collaboration with Andrei Moroianu (Paris).