Appears in collection : 2023 - T1A - WS1 - Quantum gravity and random geometry

Isoradial triangulations are example of critical planar graphs, on which discrete analyticity, integrability, discrete and continuous conformal invariance can be defined and studied for many models. I present some results on the deformations of such triangulations, which break integrability, and their effect on the critical Laplacian and some of its extensions, and for their conformal properties. The relevance and the consequence of these results for some models of two dimensional quantum gravity will be discussed.

(Joint work with J. Scott)