Alexey Kokotov

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In this paper, we introduce a new class of integrable systems, naturally associated to Hurwitz spaces (spaces of meromorphic functions over Riemann surfaces). The critical values of the meromorphic functions play the role of "times". Our systems give a natural generalization of the Ernst equation; in genus zero, they realize the scheme of deformation of(More)
Using the loop equations we find an explicit expression for genus 1 correction in hermitian two-matrix model in terms of holomorphic objects associated to spectral curve arising in large N limit. Our result generalises known expression for F 1 in hermitian one-matrix model. We discuss the relationship between F 1, Bergmann tau-function on Hurwitz spaces,(More)
Hyperbolic systems of second-order differential equations are considered in a domain with conical points at the boundary; in particular, the equations of elastodynamics are discussed. The asymptotics of solutions near conical points is studied. The “hyperbolic character” of the asymptotics shows itself in the properties of the coefficients (stress intensity(More)
We compute an the genus 1 correction to free energy of Hermitian two-matrix model in terms of theta-functions associated to spectral curve arising in large N limit. We discuss the relationship of this expression to isomonodromic tau-function, Bergmann tau-function on Hurwitz spaces, G-function of Frobenius manifolds and determinant of Laplacian in a(More)
The isomonodromic tau-function for the Hurwitz spaces of branched coverings of genus zero and one are constructed explicitly. Such spaces may be equipped with the structure of a Frobenius manifold and this introduces a flat coordinate system on the manifold. The isomonodromic taufunction, and in particular the associated G-function, are rewritten in these(More)
2 Tau-function on spaces of Abelian differentials over Riemann surfaces 7 2.1 Spaces of holomorphic differentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Variational formulas on Hg(k1, . . . , kM ) . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Basic Beltrami differentials for Hg(k1, . . . , kM ) . . . . . . . . . . . . .(More)