Vincent Bouchard

Think globally, compute locally

A bstractWe introduce a new formulation of the so-called topological recursion, that is defined globally on a compact Riemann surface. We prove that it is equivalent to the generalized recursion for spectral curves with arbitrary ramification. Using this global formulation, we also prove that the correlation functions constructed from the recursion for curves with arbitrary ramification can be obtained as suitable limits of correlation functions for curves with only simple ramification. It then follows that they both satisfy the properties that were originally proved only for curves with simple ramification.

Reconstructing WKB from topological recursion

We prove that the topological recursion reconstructs the WKB expansion of a quantum curve for all spectral curves whose Newton polygons have no interior point (and that are smooth as affine curves). This includes nearly all previously known cases in the literature, and many more; in particular, it includes many quantum curves of order greater than two. We also explore the connection between the choice of ordering in the quantization of the spectral curve and the choice of integration divisor to reconstruct the WKB expansion.

The Remodeling Conjecture and the Faber–Pandharipande Formula

In this note, we prove that the free energies Fg constructed from the Eynard–Orantin topological recursion applied to the curve mirror to

Exploring a new peak in the heterotic landscape

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String-Math 2014

reproduce the Faber–Pandharipande formula for genus g Gromov–Witten invariants of

Topological recursion and mirror curves

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