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Title:
Volumes of moduli spaces of super hyperbolic surfaces with Ramond punctures
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Abstract:
Mirzakhani produced recursion relations between polynomials that give Weil-Petersson volumes of moduli spaces of hyperbolic surfaces. Stanford and Witten described an analogous construction for moduli spaces of super hyperbolic surfaces producing Mirzakhani-like recursion relations between polynomials that give super volumes. This was achieved in the so-called Neveu-Schwarz case. Both of these stories have an algebro-geometric description and in particular this led Mirzakhani to a new proof of Witten's conjecture on intersection numbers over the moduli space of stable curves. In this lecture via the algebro-geometric description I will describe what occurs in the Ramond case of the super construction. It produces deformations of the Neveu-Schwarz polynomials again satisfying Mirzakhani-like recursion relations.
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