Orateur: Anh Minh Pham (Unige)
Titre: Perfect matchings on graphs in the Möbius band and the cylinder
Résumé:  It was proved by Lu-Wu in 1999 that the number of (weighted) perfect matchings on the 2m*4n square lattice embedded in the cylinder is equal to the square of the number of perfect matchings on the 2m*2n square lattice embedded in the Möbius band. A similar result also holds for (2m-1)*4n square lattices, with a factor 2 on the left side. In fact, these curious identities were obtained by computing and comparing exact values of the quantities on both sides, without any general underlying principle. In this talk we will give an explanation for these identities, and generalise them to big classes of graphs. These identities follow from the Pfaffian formula to count the number of perfect matchings on graphs embedded in the Möbius band. Moreover, a new proof of that formula was discovered in the course of our investigations; it is completely elementary, and we will also talk about it if time permits. (Joint work with David Cimasoni.)

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