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- W2887336437 abstract "This article discusses the connection between the matrix models and algebraic geometry. In particular, it considers three specific applications of matrix models to algebraic geometry, namely: the Kontsevich matrix model that describes intersection indices on moduli spaces of curves with marked points; the Hermitian matrix model free energy at the leading expansion order as the prepotential of the Seiberg-Witten-Whitham-Krichever hierarchy; and the other orders of free energy and resolvent expansions as symplectic invariants and possibly amplitudes of open/closed strings. The article first describes the moduli space of algebraic curves and its parameterization via the Jenkins-Strebel differentials before analysing the relation between the so-called formal matrix models (solutions of the loop equation) and algebraic hierarchies of Dijkgraaf-Witten-Whitham-Krichever type. It also presents the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations, along with higher expansion terms and symplectic invariants." @default.
- W2887336437 created "2018-08-22" @default.
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- W2887336437 date "2015-09-17" @default.
- W2887336437 modified "2023-10-16" @default.
- W2887336437 title "Algebraic geometry and matrix models" @default.
- W2887336437 doi "https://doi.org/10.1093/oxfordhb/9780198744191.013.29" @default.
- W2887336437 hasPublicationYear "2015" @default.
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