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Winter Braids Lecture Notes

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David Cimasoni
The geometry of dimer models
(The geometry of dimer models)
Winter Braids Lecture Notes, 1 : Winter Braids IV (Dijon, 2014) (2014), Exp. No. 2, 14 p., doi: 10.5802/wbln.3
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Résumé - Abstract

This is an expanded version of a three-hour minicourse given at the winterschool Winterbraids IV held in Dijon in February 2014. The aim of these lectures was to present some aspects of the dimer model to a geometrically minded audience. We spoke neither of braids nor of knots, but tried to show how several geometric tools that we know and love (e.g. (co)homology, spin structures, real algebraic curves) can be applied to very natural problems in combinatorics and statistical physics. These lecture notes do not contain any new results, but give a (relatively original) account of the works of Kasteleyn [14], Cimasoni-Reshetikhin [4] and Kenyon-Okounkov-Sheffield [16].

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