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A short overview of the "Topological recursion"
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This review is an extended version of the Seoul ICM 2014 proceedings.It is a short overview of the "topological recursion", a relation appearing in the asymptotic expansion of many integrable systems and in enumerative problems. We recall how computing large size asymptotics in random matrices, has allowed to discover some fascinating and ubiquitous geometric invariants. Specializations of this method recover many classical invariants, like Gromov--Witten invariants, or knot polynomials (Jones, HOMFLY,...). In this short review, we give some examples, give definitions, and review some properties and applications of the formalism.
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From Graph Laplacians to String Partition Functions: A Rigorous Pathway from Discrete Spectra to Emergent Geometry
Finite graphs define spectral curves that converge to stable curves in the continuum limit, connecting to topological recursion and replacing BKL singularities with nodal chains of rational curves whose entropy derive...
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