The 3-State Potts Model on Planar Maps - 07

Explore the mathematical intricacies of the 3-state Potts model applied to planar triangulations in this 48-minute conference talk. Delve into the generating function of planar triangulations where vertices are colored using three colors, weighted by size and the number of monochromatic edges. Learn how this series was proven algebraic 15 years ago through its connection to discrete differential equations (DDEs) and general algebraicity results. Discover the breakthrough determination of the exact value of this generating function, which satisfies a polynomial equation of degree in the variable. Examine the derivation of the critical value and associated exponent from this polynomial relationship. Compare this approach with the more complex case of general planar maps using 3-coloring, which yields a polynomial equation of degree 22. Gain insights into advanced combinatorial mathematics and the effective solution methods for discrete differential equations through this collaborative research with Hadrien Notarantonio from IRIF, Paris.