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Title:
Mathematical physics of map enumeration
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Abstract:
Counting problems for maps (ribbon graphs) and hypermaps (Grothendieck's "dessins d'enfants") naturally appear in various fields of mathematics and mathematical physics. It will be shown that certain generating functions associated with map and hypermap count satisfy a number of remarkable integrability properties, like Virasoro constraints, evolution equation, KP (Kadomtsev-Petviashvili) hierarchy and topological recursion in the sense of Eynard-Orantin.
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