Abstract and Keywords
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.
Keywords: matrix model, algebraic geometry, Kontsevich matrix model, moduli space, Hermitian matrix model, free energy, Seiberg-Witten-Whitham-Krichever hierarchy, symplectic invariants, formal matrix model, WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations
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