Combinatorial Maps in Critical Loop Model

by Paul Roux (ENS Paris)

Wednesday Feb 26, 2025, 10:30 AM → 11:30 AM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Seed Seminar of Mathematics and Physics

Loop models are a class of statistical lattice models whose correlation functions can be interpreted geometrically, as sums over configurations of non-intersecting loops.

In the critical limit, the observables of these models are described by a Conformal Field Theory (CFT), which is believed to be exactly solvable.

In this talk, we will shortly review what are loop models and present recent results showing that their correlation functions are related to combinatorial objects called combinatorial maps. Then, we will relate the counting of certain maps on the torus to particular classes of maps on the sphere, and explain the CFT interpretation of this mapping.

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