We review a series of forthcoming results leading to the construction of a natural evolution on the space of loops with values in a Riemannian manifold. In particular, this clarifies the algebraic structure of the renormalisation procedures appearing in the context of the theory of regularity structures.
Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions
Regularity structures and the dynamical $Φ^4_3$ model
Convergence of space-discretised gKPZ via Regularity Structures
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