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13.03.2007 (Tuesday)

Matrix models topological expansion and invariants of algebraic curves

Regular Seminar Nicolas Orantin (CEA Saclay)

16:00 Brunel U.
room M128

Considering an arbitrary algebraic curve E(x,y)=0, I will build a infinite families of invariants, Fg(E) and Wkg(E), wrt deformations of the complexe and modular structure of the curve. I will show that, when the curve is the spectral curve of a matrix model, i.e. the limit of the loop equations of the model when the size N of the matrix tends to infinity, these objects give the terms of the topological ('t Hooft) expansion of the free energy and the correlations functions of the corresponding matrix model. As an exemple, if E is the spectral curve of the hermitian 2-Matrix Model, one computes the generating functions of 2-colored discretized surfaces closed or open, with boundary operators or not.