Conformal invariance of percolation on random planar maps

Conformal invariance of critical percolation on the triangular lattice was proved by Smirnov. His proof is hard to extend to critical percolation on other lattices since his proof relies on a combinatorial identity which is only true on the triangular lattice. On random lattices known as random planar maps, however, it turns out that conformal invariance can be established. This was done in joint work with Sun, building on our earlier works with Albenque, Bernardi, Garban, Gwynne, Lawler, Li, and Sepulveda.

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