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The interface between the plus and minus phases in the low temperature 3DÌýIsing model has been intensely studied since Dobrushin’s pioneering works inÌýthe early 1970’s established its rigidity. Advances in the last five yearsÌýyielded the tightness of the maximum of this interface, in a cylinder ofÌýside length $n$, around a mean that is asymptotically $c \log(n)$ for an explicit $c$ (depending on the temperature). In this talk we will present new analogousÌýresults for the 3D Potts models. Compared to 3D Ising, the Potts model andÌýits lack of monotonicity form obstacles for existing methods, calling forÌýnew proof ideas, while its interfaces (and associated extrema) exhibitÌýricher behavior.

Joint work with Joseph Chen.Ìý